List questions from lyapunov-functions

Published on 17 Jun 2021 - 21:42

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$f: [0,1] \to [0,1],$ such that $| (f^n)'(x_0)| \leq e^{-2n}$ $\Rightarrow $ $|f^n(x_0) - f^n(x_0 + h) | \to 0,$ for $h$ small

Published on 21 Jun 2021 - 21:02

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Question about Lyapunov functions and its application on stability - Particular Example

Published on 26 Jun 2021 - 14:56

62

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How to derive this matrix identity?

Published on 28 Jun 2021 - 20:02

103

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Convergence proof of Spring Mass Damper example in Sastry's text

Published on 27 Mar 2026 - 3:41

89

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What is the difference between Lyapunov Exponent vs time and Lyapunov Exponent vs parameter?

Published on 27 Mar 2026 - 3:49

57

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Lyapunov function for $\left(\begin{array}{c}x'\\y'\end{array}\right)=\left(\begin{array}{c}x-y-x^3\\x+y-2y^3\end{array}\right)$

Published on 13 Jul 2021 - 15:50

55

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Lypanunov equation: check if a given $\Sigma$ is a solution to a Lyapunov equation? What happens for p.s.d. matrizes?

Published on 27 Jul 2021 - 10:38

99

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Show integral of function is positive definite

Published on 02 Aug 2021 - 12:27

266

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Global Lyapunov function to examine global stability?

Published on 05 Aug 2021 - 13:34

301

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Selecting a suitable Lyapunov function for the following systems to analyse global stability?

Published on 10 Aug 2021 - 14:36

87

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Finding the Lyapunov function

Published on 14 Aug 2021 - 13:13

230

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Derivative of a Lyapunov function for a nonlinear system

Published on 22 Aug 2021 - 22:10

132

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Equilibrium point of a Non linear System

Published on 25 Aug 2021 - 16:33

67

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Stability of a discrete-time non-linear system

Published on 26 Mar 2026 - 6:26

List Question

Stability in the presence of vanishing inputs

$f: [0,1] \to [0,1],$ such that $| (f^n)'(x_0)| \leq e^{-2n}$ $\Rightarrow $ $|f^n(x_0) - f^n(x_0 + h) | \to 0,$ for $h$ small

Question about Lyapunov functions and its application on stability - Particular Example

How to derive this matrix identity?

Convergence proof of Spring Mass Damper example in Sastry's text

What is the difference between Lyapunov Exponent vs time and Lyapunov Exponent vs parameter?

Lyapunov function for $\left(\begin{array}{c}x'\\y'\end{array}\right)=\left(\begin{array}{c}x-y-x^3\\x+y-2y^3\end{array}\right)$

Lypanunov equation: check if a given $\Sigma$ is a solution to a Lyapunov equation? What happens for p.s.d. matrizes?

Show integral of function is positive definite

Global Lyapunov function to examine global stability?

Selecting a suitable Lyapunov function for the following systems to analyse global stability?

Finding the Lyapunov function

Derivative of a Lyapunov function for a nonlinear system

Equilibrium point of a Non linear System

Stability of a discrete-time non-linear system

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