List questions from lyapunov-functions

Published on 12 Sep 2020 - 15:00

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When are all average trajectories of $w_{k+1}=Aw_k+b$ bounded?

Published on 12 Sep 2020 - 16:26

45

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Dissipative dynamical system

Published on 19 Sep 2020 - 10:01

53

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Existence of regular Lypanuov function for any probability measure

Published on 30 Sep 2020 - 16:54

66

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Trying to solve the Lyapunov candidate, but having trouble with some of the steps.

Published on 02 Oct 2020 - 12:30

174

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How to pick a Lyapunov Function and make asymptotically stable?

Published on 17 Oct 2020 - 18:35

46

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Reversed version of de Bruijn's identity/Boltzmann H-theorem for Markov processes

Published on 23 Feb 2026 - 11:50

309

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Comparison principle for differential equations

Published on 26 Oct 2020 - 3:10

86

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Given $dx/dt=\sin(y)+0.1\sin(x),dy/dt=-\sin(x)+0.2\sin(y)$ and $F(x,y)=\cos(x)+\cos(y)$ Determine if $F$ is a lyapunov function near $(0,0)$

Published on 30 Oct 2020 - 19:35

198

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Check if $\frac{x'^{2}}{2}-\sin(x)$ is a lyapunov function for $x''=\cos(x)-0.1x'$ near $(x,x')=(\frac{\pi}{2},0)$

Published on 30 Oct 2020 - 22:24

295

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Problem designing a control law

Published on 23 Feb 2026 - 2:34

307

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How to obtain the Lyapunov candidate of this system

Published on 06 Nov 2020 - 14:39

107

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Prove the system of ODE is asymptotically stable using Lyapunov function.

Published on 08 Nov 2020 - 19:16

53

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Complementary to Lyapunov Stability Theorem

Published on 10 Nov 2020 - 14:13

85

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How do I prove that the system is asimptotically stable under a control law?

Published on 17 Nov 2020 - 11:11

List Question

When are all trajectories of $x_{k+1}=Ax_k+b$ bounded?

When are all average trajectories of $w_{k+1}=Aw_k+b$ bounded?

Dissipative dynamical system

Existence of regular Lypanuov function for any probability measure

Trying to solve the Lyapunov candidate, but having trouble with some of the steps.

How to pick a Lyapunov Function and make asymptotically stable?

Reversed version of de Bruijn's identity/Boltzmann H-theorem for Markov processes

Comparison principle for differential equations

Given $dx/dt=\sin(y)+0.1\sin(x),dy/dt=-\sin(x)+0.2\sin(y)$ and $F(x,y)=\cos(x)+\cos(y)$ Determine if $F$ is a lyapunov function near $(0,0)$

Check if $\frac{x'^{2}}{2}-\sin(x)$ is a lyapunov function for $x''=\cos(x)-0.1x'$ near $(x,x')=(\frac{\pi}{2},0)$

Problem designing a control law

How to obtain the Lyapunov candidate of this system

Prove the system of ODE is asymptotically stable using Lyapunov function.

Complementary to Lyapunov Stability Theorem

How do I prove that the system is asimptotically stable under a control law?

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