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Finding a good Lyapunov function for $ \{ x'= y , y'= -4 x + 5x^3 - x^5 \}$

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#ordinary-differential-equations #nonlinear-system #lyapunov-functions
314
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Prove that $x_0$ is Lyapunov unstable

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#ordinary-differential-equations #dynamical-systems #stability-in-odes #lyapunov-functions
731
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How to find lyapunov function for the system?

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#ordinary-differential-equations #systems-of-equations #lyapunov-functions
130
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Finding a Lyapunov function

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#ordinary-differential-equations #lyapunov-functions
129
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LaSalle statement - Find a positive function

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#real-analysis #control-theory #nonlinear-system #stability-theory #lyapunov-functions
338
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Positive definiteness of solution to Sylvester / Lyapunov equations

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#linear-algebra #matrices #matrix-equations #stability-theory #lyapunov-functions
51
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Looking for a specific converse lyapunov theorem: Given a asymptotically stable set there exists a Lyapunov function.

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#reference-request #dynamical-systems #lyapunov-functions
604
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The asymptotic stability if the time derivative of Lyapunov function is zero

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#real-analysis #nonlinear-system #stability-theory #nonlinear-dynamics #lyapunov-functions
444
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Why the origin is globally asymptotically stable?

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#real-analysis #ordinary-differential-equations #stability-theory #lyapunov-functions
536
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Derivative of a Lyapunov function for a slowly time-varying system

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#partial-derivative #dynamical-systems #control-theory #lyapunov-functions
89
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Is a the sign of the Lyapunov exponent a sufficient condition for chaos?

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#dynamical-systems #chaos-theory #lyapunov-functions
83
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How to show the state equation that $x_1=x_2$ can only happen at the origin

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#nonlinear-system #stability-theory #nonlinear-dynamics #lyapunov-functions
811
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How to find Lyapunov function?

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#ordinary-differential-equations #stability-theory #lyapunov-functions
77
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finding a solution for a PDE equation

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#partial-differential-equations #lyapunov-functions
379
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Lyapunov stability and gradient

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#ordinary-differential-equations #partial-derivative #stability-theory #lyapunov-functions

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