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Bocher18-Jan-2012Audit:Omer Yagel084735 Control TheoryHome Assignment #10
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>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(); # input placeholderprint(); # input placeholderGiven the following Dynamic systems: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(); # input placeholderAccording to Lyapunov second method, Does the system is asymptotic stable?Given the following functions: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Which of the following functions can be Lyapunov function?
<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>According to Lyapunov second method We need Only one Equilibrium.
In our case, there are infinity Equilibrium (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmY29uc3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkxGOQ==can be any value).Hence, for this system there is no Lyapunov function.
JSFHCheck the stability of the systems using the functions you found above.
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>JSFH
According to article 1, we can not check stability for this system using Lyapunov
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=Find the values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for which the system is asymptotic stable.
<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
According to article 1, we can not check stability for this system using Lyapunov
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 1" layout="Heading 1">Question 2</Text-field>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print(); # input placeholderGiven the following 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 down the equation of state space system.
<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>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(); # input placeholderJSFH
Now we can write the matrix and vectors: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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
Choose Lyapunov function: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 set the range of the gain LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= so the system will be global asymptotic stable in closed loop.
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>At first, we will check that there is only one equilibrium:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
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(); # input placeholderFrom here we can see that if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfXzFgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfXzJgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn are zeros, then the other is also zero.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(); # input placeholderHence, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHhfXzJgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz.
We found that there is only one equilibrium.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 3" layout="Heading 3"><Font underline="true">The Lyapunov criterions:</Font></Text-field>1. We can see that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= has continuous partial derivate. 2. We will choose 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, therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= \342\210\200LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHhfXzFgRictSSNtb0dGJDYtUSIsRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiNRJ2B4X18yYEYnLUYwNi1RKyZOb3RFcXVhbDtGJ0YzRjYvRjpGOEY8Rj5GQEZCRkQvRkdRLDAuMjc3Nzc3OGVtRicvRkpGVC1JI21uR0YkNiRRIjBGJ0YzRjM=.3. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYsLUYsNiNRJ2B4X18xYEYnLUY2NiQtRiw2JVEidEYnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI9RidGQi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSi8lKXN0cmV0Y2h5R0ZKLyUqc3ltbWV0cmljR0ZKLyUobGFyZ2VvcEdGSi8lLm1vdmFibGVsaW1pdHNHRkovJSdhY2NlbnRHRkovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZLUkjbW5HRiQ2JFEiMEYnRkItRkU2LVEiLEYnRkJGSC9GTEYxRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5RLDAuMzMzMzMzM2VtRictRiM2JC1GLDYjUSdgeF9fMmBGJ0Y9RkRGZm5Gam4tRiw2JVEiVkYnRi9GMkZC = print(); # input placeholder4. 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 = print(); # input placeholder5. 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(); # input 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(); # input placeholderWe know that the solution is look like: 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 . we will build LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, and compare coefficients to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZXEzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw==: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(); # input placeholderFrom here we can see: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print(); # input placeholderSo now we have the matrix 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print(); # input placeholderFor stability, we want LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkUFNERicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== :Not all primary Minors are non-negative:
We know that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, and we choosed LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHBfXzFgRictSSNtb0dGJDYtUSI+RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEsRGV0ZXJtaW5hbnRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJRRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RLyZHcmVhdGVyRXF1YWw7RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JFEiMEYnRj0=print(); # input 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(); # input placeholderBoth 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 therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=6. 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\342\210\200LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=
The function fulfill All the 6 Lyapunov criterions - the function global asymptotic stable for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.
Check the answer in article 2 using any method you know.
<Text-field style="Heading 2" layout="Heading 2">Art. 3</Text-field>I will check it using Routh Horowitz table: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print(); # input placeholderJSFH
JSFH
<Text-field style="Heading 1" layout="Heading 1">Question 3</Text-field>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print(); # input placeholderGiven the following Non linear system: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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=Check asymptotic and global asymptotic stability of the system Equilibrium at the Origin, using Lyapunov.
<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>At first, we will check that there is only one equilibrium:JSFH
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(); # input placeholderFrom here we can see that if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfXzFgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfXzJgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn are zeros, then the other is also zero.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(); # input placeholderFrom here we can see that if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYHhfXzFgRic= or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYHhfXzJgRic= are zeros, then the other is also zero.
We found that there is only one equilibrium.Now we build function that is Non-negative for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHhfXzFgRictSSNtb0dGJDYtUSIsRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiNRJ2B4X18yYEYnRjM=, with continuous partial derivate at the origin.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print(); # input placeholderNow we want the derivate of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= to be smaller than zero: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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnZXhwYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVElc3Vic0YnRi9GMi1GNjYkLUYjNictRiw2JVEkZXExRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZMLyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSRlcTJGJ0YvRjJGRC1GLDYjUSlgVl9fZG90YEYnRkhGSC1GRTYtUSFGJ0ZIRkovRk5GTEZPRlFGU0ZVRlcvRlpRLDAuMjc3Nzc3OGVtRicvRmduRmRvprint(); # input 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print(); # input placeholderFrom here we can see that the coefficient of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is non-negative. We will set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0Y5LUYjNiMtRlM2JFEiMkYnRjkvJS5saW5ldGhpY2tuZXNzR0ZVLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmluLyUpYmV2ZWxsZWRHRj0tRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZlby1GLDYlUSJiRidGL0YyRjVGT0Zebw==So we got: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FqdywoKiYsJiomLUkleF9fMUc2IjYjSSJ0RzYiIiIlSSJhRzYiIiIiIiIjKiYtSSV4X18yRzYiNiNJInRHNiIiIiVJImJHNiIiIiIiIiMiIiJJJmFscGhhRzYiIiIiIiIiKihJImFHNiIiIiItSSV4X18xRzYiNiNJInRHNiIiIiItSSV4X18yRzYiNiNJInRHNiIiIiIhIiMqKEkiYkc2IiIiIi1JJXhfXzFHNiI2I0kidEc2IiIiIi1JJXhfXzJHNiI2I0kidEc2IiIiIiIiI0YnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDEzNjM1KUYnLyUldmlld0dRJmxhYmVsRictRiw2LVEiPEYnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSSNtbkdGJDYkUSIwRidGLw==print(); # input placeholderAnd from here we know that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSI8RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSIwRidGMg==print(); # input placeholderUntil this point we fulfill the 3 criterions of Lyapunov first method - the system is asymptotic stable around the Origin.To check if the system is global asymptotic around the Origin, we will check: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print(); # input placeholder
Hence, The system is global asymptotic stable around the Origin for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EvMkkmYWxwaGFHNiIiIiFGJy8lK2FjdGlvbnR5cGVHUTxtYXBsZXNvZnQuY29tOmxhYmVsKEwxMzYxMylGJy8lJXZpZXdHUSZsYWJlbEYnRis=print(); # input placeholder
Does equilibrium at the Origin is asymptotic / global asymptotic for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyRjI= ?
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSomY29sb25lcTtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyLUY2Ni1RIjpGJ0YyRjlGO0Y9Rj9GQUZDRkVGR0ZKprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkZXExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy1GLDYlUSRlcTJGJ0YvRjI=print(); # input 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(); # input placeholderWe will check stability with two different methods:
Routh 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print(); # input 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(); # input placeholderHence, the system is unstable for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyRjI=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(); # input 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print(); # input placeholderFrom here you can see that there are infinite options to get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EqYFZfX2RvdDJgRictSSNtb0dGJDYtUSI8RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz. Hence, the system is unstable for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyRjI=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>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(); # input placeholderGiven the following Non linear system:QyY+SSRlcTFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JJXhfXzFHRiU2I0kidEdGJUYuLUkleF9fMkdGJUYtISIiPkkkZXEyR0YlLy1GKDYkRi9GLiwmRi9GMSokRisiIiRGMUYxprint(); # input placeholderFind the system equilibrium. Does it is the only equilibrium?
<Text-field style="Heading 2" layout="Heading 2">Art. 1</Text-field>At first, we will check that there is only one equilibrium:JSFH
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LUkoaXNvbGF0ZUc2IjYkLUklc3Vic0clKnByb3RlY3RlZEc2JC8tSSVkaWZmR0YoNiQtSSV4X18xR0YkNiNJInRHRiRGMSIiIUkkZXExR0YkLUkleF9fMkdGJEYwprint(); # input placeholderLUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUklc3Vic0dGJTYkLy1JJWRpZmZHRiU2JC1JJXhfXzJHRic2I0kidEdGJ0YzIiIhSSRlcTJHRidGMA==print(); # input placeholderFrom here we can see that if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EnYHhfXzJgRic= is zero, then LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHhfXzFgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtbkdGJDYkUSIwRidGM0Yz.
We found that there is only one equilibrium, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYHhfXzFgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EnYHhfXzJgRidGLy1JI21uR0YkNiRRIjBGJ0YzRjM=
Check asymptotic and global asymptotic stability of the equilibrium you found in article 1 according to the following functions: Qyg+SSVWX18xRzYiLCYqJC1JJXhfXzFHRiU2I0kidEdGJSIiIyIiIiokLUkleF9fMkdGJUYqRixGLSEiIj5JJVZfXzJHRiUsJiokLCZGKEYtRi9GLUYsRi1GLkYtRjE+SSVWX18zR0YlLChGNUYtRi5GLSokRigiIiVGLUYxLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 2" layout="Heading 2">Art. 2</Text-field>
<Text-field style="Heading 3" layout="Heading 3"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>As we can see, the function and it's partial derivate are continuous around the Origin. The function is positive for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.We will check LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzF+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw==:PkkpVl9fMX5kb3RHNiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSVWX18xR0YkSSJ0R0Ykprint(); # input placeholderLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJDYlSSRlcTFHNiJJJGVxMkdGKkkpVl9fMX5kb3RHRio=print(); # input placeholderLUkoY29sbGVjdEc2IjYkLCgqJi1JJXhfXzFHRiQ2I0kidEdGJCIiIi1JJXhfXzJHRiRGKkYsIiIjKiRGLUYvISIjKiZGLUYsRigiIiRGMUYuprint(); # input placeholder
There are infinite combinations for which we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzF+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw==Hence - we cannot check stability for this function.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 3" layout="Heading 3"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EnYFZfXzJgRictSSNtb0dGJDYvUSI9RicvJStleGVjdXRhYmxlR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTS1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2Ji1GIzYqLUklbXN1YkdGJDYlLUYsNidRInhGJy8lJ2l0YWxpY0dGNUYzRjYvRjpRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYmUSIxRidGM0Y2RjlGM0Y2RjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GVDYmLUYjNiYtRiw2J1EidEYnRmhuRjNGNkZqbkYzRjZGOUYzRjZGOS1GMDYvUSIrRidGM0Y2RjlGPEY/RkFGQ0ZFRkdGSS9GTFEsMC4yMjIyMjIyZW1GJy9GT0ZgcC1GWTYlRmVuLUYjNiYtRl9vNiZRIjJGJ0YzRjZGOUYzRjZGOUZib0Zlb0YzRjZGOUYzRjZGOUZkcC8lMXN1cGVyc2NyaXB0c2hpZnRHRmRvRlxwLUZRNiUtRlQ2Ji1GIzYnRmJwRmVvRjNGNkY5RjNGNkY5RmRwRmlwRjNGNkY5">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</Equation></Text-field>As we can see, the function and it's partial derivate are continuous around the Origin. The function is positive for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.We will check LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzJ+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw==:PkkpVl9fMn5kb3RHNiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSVWX18yR0YkSSJ0R0Ykprint(); # input placeholderLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJDYlSSRlcTFHNiJJJGVxMkdGKkkpVl9fMn5kb3RHRio=print(); # input placeholderMiwkLUklc29ydEclKnByb3RlY3RlZEc2IywoKiQtSSV4X18xRzYiNiNJInRHRiwiIiUhIiMqJkYqIiIkLUkleF9fMkdGLEYtIiIiISIlKiRGMyIiI0YwIyEiIkY4IiIhprint(); # input placeholderLUkoaXNvbGF0ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkMiwoKiQtSSV4X18xR0YnNiNJInRHRiciIiUiIiIqJkYsIiIkLUkleF9fMkdGJ0YuRjEiIiMqJEY0RjZGMSIiIUYyprint(); # input placeholder
There are infinite combinations for which we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzJ+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw==Hence - we cannot check stability for this function.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=
<Text-field style="Heading 3" layout="Heading 3"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>As we can see, the function and it's partial derivate are continuous around the Origin. The function is positive for every LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=.We will check LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzJ+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw==:PkkpVl9fM35kb3RHNiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSVWX18zR0YkSSJ0R0Ykprint(); # input placeholderLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJDYlSSRlcTFHNiJJJGVxMkdGKkkpVl9fM35kb3RHRio=print(); # input placeholderFrom here we can see that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1ErYFZfXzN+ZG90YEYnLUkjbW9HRiQ2LVEiPEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbW5HRiQ2JFEiMEYnRjNGMw== for every value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHhfXzFgRictSSNtb0dGJDYtUSIsRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiNRJ2B4X18yYEYnRjM= . Hence, the system is asymptotic stable.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM=Pkk0Vl9fM354JnJhcnI7JmluZmluO0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiUvLUkleF9fMUdGJDYjSSJ0R0YkSSlpbmZpbml0eUdGJy8tSSV4X18yR0YkRixGLkklVl9fM0dGJA==print(); # input placeholder