<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>

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Author:

Itamar Bocher

18-Jan-2012

Audit:

Omer Yagel

084735 Control Theory

Home Assignment #11

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=

<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>

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

print(); # input placeholder

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Given the following Dynamic system in the state space:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

We want to design optimal regulator using the state feedback

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

that minimize the following criterion:

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

Find the gain feedback matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUSlgS19fb3B0YEYnRjk=.

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

The equation of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EpYEtfX29wdGBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= is:

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JSFH

We will find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= from Riccati equation. To solve the Riccati equation we will find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiUUYnRi9GMkY5 :

In the price function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= , the expression 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 equal to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtRiM2Ki1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInlGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiM2JC1GTDYlUSJURidGT0ZSRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYsNi1RIi5GJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVGam4tRkw2JVEiUUYnRk9GUkZmbkZLLUYsNi1RIj1GJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUZJNiUtSShtZmVuY2VkR0YkNiQtRiM2JUZLLUZlbzYkLUYjNiQtRkw2JVEidEYnRk9GUkYvRi9GL0YvLUYjNiQtSSNtbkdGJDYkUSIyRidGL0YvRllGL0YrRi8=

Hence, we will choose LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= that is PSD:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

print(); # input placeholder

Finding LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

In the price function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= , the expression 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 equal to 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

Hence, we will choose LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= that is PSD:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShSaWNjYXRpR0YoLy1JJ1JUQUJMRUdGKDYlIjUnM2NzT3VTdVklPS1JJ01BVFJJWEdGKDYjNyQ3JCwqKiZJI3gyR0YoIiIiSSN4M0dGKEY7ISQrIkY6ISIjRjxGPkY7RjssKiomRjpGO0kjeDRHRihGO0Y9SSN4MUdGKEY7RjohIiRGQUY+NyQsKiomRjxGO0ZBRjtGPUZCRjtGPEZDRkFGPiwqKiRGQSIiI0Y9RjpGO0Y8RjtGQSEiJ0knTWF0cml4R0YlLUYwNiUiNVVCRW5WMlduVz0tRjQ2IzckNyQiIiFGU0ZSRks3Iy8tRks2Iy9JJCVpZEdGKEYyLUZLNiMvRllGTg==

Solving the system:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PCYvSSN4MUc2IiQiK3lIRFJYISM1L0kjeDJHRiUkIitEIVIhKT4pISM2L0kjeDNHRiVGKy9JI3g0R0YlJCIrZUBYUj9GLQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJQR0YoLUknUlRBQkxFR0YoNiUiNWF3QW5WMlduVz0tSSdNQVRSSVhHRig2IzckNyQkIit5SERSWCEjNSQiK0QhUiEpPikhIzY3JEY6JCIrZUBYUj9GPEknTWF0cml4R0YlNyMtRkA2Iy9JJCVpZEdGKEYx

Hence,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdLX19vcHRHRigtSSdSVEFCTEVHRig2JSI1OSdHc091U3VZJT0tSSdWRUNUT1JHRig2IzckJCIwKytdLVIhKT4pISM6JCIwKyshZUBYUj9GOCZJJ1ZlY3RvckdGJTYjSSRyb3dHRig3Iy1GOzYjL0kkJWlkR0YoRjE=

Now, the following control law is activated on the system:

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ1R0YoLCgtSSV4X18xR0YoNiNJInRHRigkITArK10tUiEpPikhIzotSSV4X18yR0YoRjEkITArKyFlQFhSP0Y1SSJyR0YoIiIiNyMsKEYvXUJGRUEzQkQ1NjRDQkRDOEVGNl1CRkNBMUFFMDc4MDRCMTVDRjpGOw==

Where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is an entrance.

Find the transfer function between LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== in closed loop.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

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

The state space is now:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTVHRigvSSd4X19kb3RHRigsJiomSSJhR0YoIiIiSSJ4R0YoRjNGMyomSSJiR0YoRjMsJiomSSdrX19vcHRHRihGM0Y0RjMhIiJJInJHRihGM0YzRjM3I0Yu

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kneF9fZG90RzYiLCYqJiwmKiZJImJHRiQiIiJJJ2tfX29wdEdGJEYqISIiSSJhR0YkRipGKkkieEdGJEYqRioqJkYpRipJInJHRiRGKkYq

From here we got that

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

print(); # input placeholder

JSFH

Now we use the following relation (this relation was shown in dynamic system formula sheet):

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvSSJZR0YoLCQqJiwoKiRJInNHRigiIiMiIiJGMiQiMCsrIWVAWFJdISM5JCIwKytEIVIhKT41ISM4RjQhIiJJIlVHRihGNCQiIzUiIiE3Iy9GLSwkKiYsKEYxRjRGMl00MDE0Mjg2NjI1ODE3NzZEXTQwMjQ2NTY1NUVGRjY5RDlGNEY7RjxGNF00MDI0MDAwMDAwMDAwMDAw

JSFH

The transfer function is:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvKiZJIlVHRighIiJJIllHRigiIiIsJCokLCgqJEkic0dGKCIiI0YxRjYkIjArKyFlQFhSXSEjOSQiMCsrRCFSISk+NSEjOEYxRi8kIiM1IiIhNyMvRi0sJCokLChGNUYxRjZdNDAxNDI4NjYyNTgxNzc2RF00MDI0NjU2NTVFRkY2OUQ5RjFGL100MDI0MDAwMDAwMDAwMDAw

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>

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

print(); # input placeholder

Given the following system:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=

NiUvLUkieEc2IjYjIiIhSSV4X18wR0YmSSJhR0YmMkYoSSJiR0Ym

With the price function:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

MiIiIUkickc2Ig==

MiIiIUkicUc2Ig==

Where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRInJGJ0YvRjJGNS1GLDYlUSJxRidGL0YyRjUtRiw2I1EnYHhfXzBgRidGOQ== are known scalar parameters. The gain LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is unknown.

Find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= that minimize the price function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRInJGJ0YvRjJGNS1GLDYlUSJxRidGL0YyRjUtRiw2I1EnYHhfXzBgRidGOQ==

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

From the given data:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShSaWNjYXRpR0YoLywoKiZJImFHRigiIiJJIlBHRihGMiIiIyooRjNGNEkiYkdGKEY0SSJyR0YoISIiRjhJInFHRihGMiIiITcjRi4=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUShSaWNjYXRpRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJQRidGL0YyRkE=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQqJiwmKiZJImFHNiIiIiJJInJHRidGKEYoKiQsJiomRiYiIiNGKUYtRigqKEkiYkdGJ0YtSSJxR0YnRihGKUYoRigjRihGLUYoRihGLyEiIywkKiYsJkYlISIiRipGKEYoRi9GMkY2

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJQR0YoKiYsJiomSSJhR0YoIiIiSSJyR0YoRjJGMiokLCYqJkYxIiIjRjNGN0YyKihJImJHRihGN0kicUdGKEYyRjNGMkYyI0YyRjdGMkYyRjkhIiM3I0Yu

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJLR0YoKigsJiomSSJhR0YoIiIiSSJyR0YoRjJGMiokLCYqJkYxIiIjRjNGN0YyKihJImJHRihGN0kicUdGKEYyRjNGMkYyI0YyRjdGMkYyRjkhIiJGM0Y8NyNGLg==

Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= you found above. write it as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRInJGJ0YvRjJGNS1GLDYlUSJxRidGL0YyRjUtRiw2I1EnYHhfXzBgRidGOQ==.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTJHRigvSSJ1R0YoLCQqJkkia0dGKCIiIkkieEdGKEYzISIiNyNGLg==

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

KiYtSSdzaWdudW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKihJImtHRigiIiNJInJHRigiIiJJInhHRihGLUYvKiZJInFHRihGL0YwRi1GL0YvSSlpbmZpbml0eUdGJkYv

From Lyapunov we know:

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

Hence, in our system:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdKX19vcHRHRigqKEk3I21zdWIobWkoIngiKSxtbigiMCIpKUdGKCIiIywmKiZJImFHRigiIiJJInJHRihGNEY0KiQsJiomRjNGMEY1RjBGNCooSSJiR0YoRjBJInFHRihGNEY1RjRGNCNGNEYwRjRGNEY6ISIjNyNGLg==

<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlMtRiw2JVEld2l0aEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUY2Ni1RIUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiM2Iy1GLDYlUS5MaW5lYXJBbGdlYnJhRidGL0YyRmduRjlGNS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZTLyUmZGVwdGhHRmRvLyUqbGluZWJyZWFrR1EobmV3bGluZUYnRk9GVS1GWTYkLUYjNiVGZ24tRiM2Iy1GLDYlUS9EeW5hbWljU3lzdGVtc0YnRi9GMkZnbkY5RjVGX29GX28tRiw2JVEqaW50ZXJmYWNlRidGL0YyLUZZNiQtRiM2JS1GLDYlUSx0eXBlc2V0dGluZ0YnRi9GMi1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GLDYlUSlleHRlbmRlZEYnRi9GMkY5RjVGTw==

print(); # input placeholder

Given the following system:

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JzY3JpcHQ9ImZhbHNlIiBmYW1pbHk9IlRpbWVzIE5ldyBSb21hbiIgb3BhcXVlPSJmYWxzZSIgdW5kZXJsaW5lPSJmYWxzZSIgYmFja2dyb3VuZD0iWzI1NSwyNTUsMjU1XSIgcmVhZG9ubHk9ImZhbHNlIiBmb3JlZ3JvdW5kPSJbMCwwLDBdIiBhbGlnbm1lbnQ9ImxlZnQiIGZpcnN0aW5kZW50PSIwIiBzcGFjZWJlbG93PSIwIiBsZWZ0bWFyZ2luPSIwIiBsaW5lc3BhY2luZz0iMC4wIiBpbml0aWFsPSIwIiBsaW5lYnJlYWs9InNwYWNlIiByaWdodG1hcmdpbj0iMCIgYnVsbGV0c3VmZml4PSIiIHNwYWNlYWJvdmU9IjAiIGJ1bGxldD0ibm9uZSIgcGFnZWJyZWFrLWJlZm9yZT0iZmFsc2UiPjxFcXVhdGlvbiBleGVjdXRhYmxlPSJmYWxzZSIgaW5wdXQtZXF1YXRpb249IiIgZGlzcGxheT0iTFVrbGJYSnZkMGMySXk5SksyMXZaSFZzWlc1aGJXVkhOaUpKTEZSNWNHVnpaWFIwYVc1blIwa29YM041YzJ4cFlrZEdKelkxTFVramJXbEhSaVEyTmxFaWVrWW5MeVVuWm1GdGFXeDVSMUV3VkdsdFpYTitUbVYzZmxKdmJXRnVSaWN2SlNWemFYcGxSMUVqTVRSR0p5OGxKV0p2YkdSSFVTVjBjblZsUmljdkpTZHBkR0ZzYVdOSFVTWm1ZV3h6WlVZbkx5VXFkVzVrWlhKc2FXNWxSMFk2THlVcWMzVmljMk55YVhCMFIwWTZMeVVzYzNWd1pYSnpZM0pwY0hSSFJqb3ZKU3RtYjNKbFozSnZkVzVrUjFFb1d6QXNNQ3d3WFVZbkx5VXJZbUZqYTJkeWIzVnVaRWRSTGxzeU5UVXNNalUxTERJMU5WMUdKeThsSjI5d1lYRjFaVWRHT2k4bEsyVjRaV04xZEdGaWJHVkhSam92SlNseVpXRmtiMjVzZVVkR09pOGxLV052YlhCdmMyVmtSMFk2THlVcVkyOXVkbVZ5ZEdWa1IwWTZMeVVyYVcxelpXeGxZM1JsWkVkR09pOGxMSEJzWVdObGFHOXNaR1Z5UjBZNkx5VTJjMlZzWldOMGFXOXVMWEJzWVdObGFHOXNaR1Z5UjBZNkx5VXNiV0YwYUhaaGNtbGhiblJIVVNWaWIyeGtSaWN2SlN0bWIyNTBkMlZwWjJoMFIwWlpSaTh2UmpOUkl6RXlSaWN2UmpaR09rWTRSanRHUFVZL1JrRkdSRVpIUmtsR1MwWk5SazlHVVVaVFJsVXZSbGhSSjI1dmNtMWhiRVluIj5MVWtsYlhKdmQwYzJJeTlKSzIxdlpIVnNaVzVoYldWSE5pSkpMRlI1Y0dWelpYUjBhVzVuUjBrb1gzTjVjMnhwWWtkR0p6WTFMVWtqYldsSFJpUTJObEVpZWtZbkx5VW5abUZ0YVd4NVIxRXdWR2x0WlhOK1RtVjNmbEp2YldGdVJpY3ZKU1Z6YVhwbFIxRWpNVFJHSnk4bEpXSnZiR1JIVVNWMGNuVmxSaWN2SlNkcGRHRnNhV05IVVNabVlXeHpaVVluTHlVcWRXNWtaWEpzYVc1bFIwWTZMeVVxYzNWaWMyTnlhWEIwUjBZNkx5VXNjM1Z3WlhKelkzSnBjSFJIUmpvdkpTdG1iM0psWjNKdmRXNWtSMUVvV3pBc01Dd3dYVVluTHlVclltRmphMmR5YjNWdVpFZFJMbHN5TlRVc01qVTFMREkxTlYxR0p5OGxKMjl3WVhGMVpVZEdPaThsSzJWNFpXTjFkR0ZpYkdWSFJqb3ZKU2x5WldGa2IyNXNlVWRHT2k4bEtXTnZiWEJ2YzJWa1IwWTZMeVVxWTI5dWRtVnlkR1ZrUjBZNkx5VXJhVzF6Wld4bFkzUmxaRWRHT2k4bExIQnNZV05sYUc5c1pHVnlSMFk2THlVMmMyVnNaV04wYVc5dUxYQnNZV05sYUc5c1pHVnlSMFk2THlVc2JXRjBhSFpoY21saGJuUkhVU1ZpYjJ4a1JpY3ZKU3RtYjI1MGQyVnBaMmgwUjBaWlJpOHZSak5SSXpFeVJpY3ZSalpHT2tZNFJqdEdQVVkvUmtGR1JFWkhSa2xHUzBaTlJrOUdVVVpUUmxVdlJsaFJKMjV2Y20xaGJFWW48L0VxdWF0aW9uPjwvVGV4dC1maWVsZD4=Fbt

QyQ+SSJHRzYiKiQsJkkic0dGJSIiIiEiIkYpRipGKg==

The system entrance is

QyQ+SSJyRzYiIiIhISIi

The initial conditions of the system are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVRjpGPg==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVRjpGPg==.

Calculate the gain LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= so when reacting the initial conditions, the price criterion LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtaUdGJDYlUSJKRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y4USdub3JtYWxGJ0Y6Rjo= will be reduced.

QyQ+SSJKRzYiLUkkaW50R0YlNiQqJC1JInVHRiU2I0kidEdGJSIiIy9GLTsiIiFJKWluZmluaXR5RyUqcHJvdGVjdGVkRyEiIg==

print(); # input placeholder

<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>

Qyg+SSRlcTFHNiIvSSJ1R0YlLCYqJkkiS0dGJSIiIkkieUdGJUYrISIiSSJ6R0YlRitGLT5JJGVxMkdGJS9GLComSSJHR0YlRitGJ0YrRi0+SSRlcTNHRiUvRi4sJCooSSJzR0YlRi1GKkYrRixGK0YtRi0=

A bit of algebraic games to write the system equations:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJDYkLUkoaXNvbGF0ZUc2IjYkSSRlcTJHRitJInVHRitJJGVxMUdGKw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywmKiZJInNHNiIiIiJJInlHRiZGJ0YnRighIiIsJiomSSJLR0YmRidGKEYnRilJInpHRiZGJw==

LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkoYWxnc3Vic0dGJzYkLyomSSJ5R0YnIiIiSSJzR0YnRi9JJ3lfX2RvdEdGJy8sJiomRjBGL0YuRi9GL0YuISIiLCYqJkkiS0dGJ0YvRi5GL0Y1SSJ6R0YnRi9GMQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kneV9fZG90RzYiLCgqJkkiS0dGJCIiIkkieUdGJEYoISIiRilGKEkiekdGJEYo

LUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkoYWxnc3Vic0dGJDYkLyomSSJ6R0YnIiIiSSJzR0YnRi9JJ3pfX2RvdEdGJyomSSRlcTNHRidGL0YwRi9GMQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0knel9fZG90RzYiLCQqJkkiS0dGJCIiIkkieUdGJEYoISIi

And now we can generate the matrix:

QyY+NiRJIkFHNiJJJ3hfX2RvdEdGJi1JL0dlbmVyYXRlTWF0cml4R0YmNiQ3JC9JJ3lfX2RvdEdGJiwoKiZJIktHRiYiIiJJInlHRiZGMSEiIkYyRjFJInpHRiZGMS9JJ3pfX2RvdEdGJiwkRi9GMzckRjJGNEYxPkkieEdGJi0mSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0knY29sdW1uR0YmNiMvSSQlaWRHRiYiNWUiR2ZQdVN1WSU9RjM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+NiRJIkFHRihJJ3hfX2RvdEdGKDYkLUknUlRBQkxFR0YoNiUiNSlSR2ZQdVN1WSU9LUknTUFUUklYR0YoNiM3JDckLCZJIktHRigiIiIhIiJGPEY9NyRGOyIiIUknTWF0cml4R0YlLUYyNiUiNXkjR2ZQdVN1WSU9LUY2NiM3JDcjLCRJJ3lfX2RvdEdGKEY9NyMsJEknel9fZG90R0YoRj0mSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyQtRkA2Iy9JJCVpZEdGKEY0LUZNNiMvRlVGQw==

According to Lyapunov, 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=

We will choose

QyQ+SSJRRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiNXklSGZQdVN1WSU9ISIi

We will find it from the price function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

Notice that

LyokLUkidUc2IjYjSSJ0R0YmIiIjLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjKiQtSSRyaHNHRiw2I0kkZXExR0YmRik=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LyokLUkidUc2IjYjSSJ0R0YmIiIjLCgqJkkiS0dGJkYpSSJ5R0YmRikiIiIqKEYsRi5GLUYuSSJ6R0YmRi4hIiMqJEYwRilGLg==

LUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUkwZGVsYXlEb3RQcm9kdWN0RzYkRiQvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYkSShfc3lzbGliR0YrNiQtRic2JC0mSSdWZWN0b3JHRi02I0kkcm93R0YrNiMvSSQlaWRHRisiNS1QI2ZQdVN1WSU9LUknTWF0cml4R0YtNiMvRjkiNUFRI2ZQdVN1WSU9LSZGNDYjSSdjb2x1bW5HRis2Iy9GOSI1VVIjZlB1U3VZJT0=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCoqJkkjUTFHNiIiIiJJInlHRiUiIiNGJiooSSNRMkdGJUYmRidGJkkiekdGJUYmRiYqKEkjUTNHRiVGJkYnRiZGK0YmRiYqJkkjUTRHRiVGJkYrRihGJg==

Comparing coefficients:

Pkkkc29sRzYiPCYvSSNRMUdGJCokSSJLR0YkIiIjL0kjUTJHRiQsJEYpISIiL0kjUTNHRiRGLS9JI1E0R0YkIiIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig8Ji9JI1ExR0YoKiRJIktHRigiIiMvSSNRMkdGKCwkRjIhIiIvSSNRM0dGKEY2L0kjUTRHRigiIiI3I0Yu

PkkiUUc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiRJJHNvbEdGJEYj

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJRR0YoLUknUlRBQkxFR0YoNiUiNSczP2ZQdVN1WSU9LUknTUFUUklYR0YoNiM3JDckKiRJIktHRigiIiMsJEY4ISIiNyRGOiIiIkknTWF0cml4R0YlNyMtRj42Iy9JJCVpZEdGKEYx

Now we will find

QyQ+SSJQRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiNTEzI2ZQdVN1WSU9ISIi

QyQ+SSRlcTRHNiIvLCYtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSSxUeXBlc2V0dGluZ0c2JEYrSShfc3lzbGliR0YlNiQpSSJBR0YlSSMlVEdGJUkiUEdGJSIiIi1GKTYkRjVGM0Y2LCRJIlFHRiUhIiJGOw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

QyQ+SSVzb2wxRzYiLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JDwmLyYtSSRsaHNHRik2I0kkZXE0R0YlNiQiIiJGNCYtSSRyaHNHRilGMUYzLyZGLzYkRjQiIiMmRjZGOi8mRi82JEY7RjQmRjZGPy8mRi82JEY7RjsmRjZGQzwmSSNQMUdGJUkjUDJHRiVJI1AzR0YlSSNQNEdGJSEiIg==

print(); # input placeholder

PkkiUEc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiRJJXNvbDFHRiRGIw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJQR0YoLUknUlRBQkxFR0YoNiUiNSE+OWZQdVN1WSU9LUknTUFUUklYR0YoNiM3JDckLCQqKEkiS0dGKCIiIiwmRjlGOkY6RjpGOiwmRjlGOiEiIkY6Rj0jRj0iIiMjRjpGPzckRkAsJCooRjtGOkY5Rj1GPEY9Rj5JJ01hdHJpeEdGJTcjLUZENiMvSSQlaWRHRihGMQ==

We demand that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= will be PD: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=

NiQtSSI+RyUqcHJvdGVjdGVkRzYkLUksRGV0ZXJtaW5hbnRHNiI2I0kiUEdGKSIiIUkiS0dGKQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQyIiIhKiZJIktHNiIiIiIsJkYmRighIiJGKCEiI0Ym

We got LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.

QyQtSSI+RyUqcHJvdGVjdGVkRzYkKiZJJ2Fzc3VtZUc2JEYlSShfc3lzbGliRzYiIiIiSSJLR0YrRiwiIiEhIiI=

Now we define

QyQ+SSV4X18wRzYiLSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSdjb2x1bW5HRiU2Iy9JJCVpZEdGJSI1JVxLZlB1U3VZJT0hIiI=

PkkiSkc2Ii1JMGRlbGF5RG90UHJvZHVjdEc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiRJLFR5cGVzZXR0aW5nRzYkRihJKF9zeXNsaWJHRiQ2JC1GJjYkKUkleF9fMEdGJEkjJVRHRiRJIlBHRiRGMg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJKR0YoLCQqKkkiS0dGKCIiIiwmRjBGMUYxRjFGMSwmRjBGMSEiIkYxRjRJJXlfXzBHRigiIiMjRjRGNjcjRi4=

We will minimize LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

Pkklc29sMkc2Ii1JKWFzc3VtaW5nR0koX3N5c2xpYkdGJDYkNyMtSSZzb2x2ZUc2JCUqcHJvdGVjdGVkR0YnNiMtSSlzaW1wbGlmeUdGLDYkLy1JJWRpZmZHRi02JEkiSkdGJEkiS0dGJCIiIUY3NyMtSSI+R0YtNiRGN0Y4

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVzb2wyR0YoNiU8JC9JIktHRihGMS9JJXlfXzBHRigiIiE8JC9GMSwmIiIiRjgqJCIiIyNGOEY6RjgvRjNGMzwkL0YxLCZGOEY4RjkhIiJGPDclRi9GNUY9

JSFH

Knowing that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=:

PkkiS0c2Ii1JJHJoc0clKnByb3RlY3RlZEc2IyZJJXNvbDJHRiQ2JCIiIyIiIg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJLR0YoLCYiIiJGLyokIiIjI0YvRjFGLzcjRi4=

Find the system poles for the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= you found above.

<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>

Having the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= we can find

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1KVJHZlB1U3VZJT0tSSdNQVRSSVhHRig2IzckNyQsJiZJJXNvbDJHRig2IyIiIyIiIiEiIkY6Rjs3JEY2IiIhSSdNYXRyaXhHRiU3Iy1GPjYjL0kkJWlkR0YoRi8=

QyQ+SSNJTUc2Ii1JL0lkZW50aXR5TWF0cml4R0YlNiMiIiMhIiI=

LUksRGV0ZXJtaW5hbnRHNiI2IywmKiZJI0lNR0YkIiIiSSJzR0YkRilGKUkiQUdGJCEiIg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCoqJkkic0c2IiIiIiIiIyNGJkYnISIiKiRGJEYnRiYqJEYnRihGJkYmRiY=

The poles of the system are:

LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSSZzb2x2ZUc2JEYkSShfc3lzbGliRzYiNiQvLCoqJkkic0dGKiIiIiIiIyNGMEYxISIiKiRGL0YxRjAqJEYxRjJGMEYwRjAiIiFGLw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiReJCQiKzV5MXJxISM1JCIrcTViJFEiISIqXiRGJCQhK3E1YiRRIkYp

JSFH