Global asymptotic stability (GAS) follows similarly. ... This example shows a system where a Lyapunov function can be used to prove Lyapunov stability but cannot ... History · Stability for linear state space... · Example

A Lyapunov global asymptotic stability theorem suppose there is a function V ... let's use Lyapunov theorem to show it's globally asymptotically stable.

This theorem proves that global uniform asymptotic stability of the linearization implies local uniform asymptotic stability of the original nonlinear system.

Definition [Global asymptotic stability]. The equilibrium state 0 of (1) is globally asymptotically stable, if it is asymptotically stable for any ′ > δ 0 ...

13 авг. 2020 г. · An equilibrium is called globally stable, if it is stable for (almost) all initial conditions, not just some which are close to the equilibrium y∗. Global Asymptotic stability of an ODE system? Lyapunov function to prove globally asymptotically stable Другие результаты с сайта math.stackexchange.com

Lyapunov stability theorem is a basic tool for stability analysis, and it gives sufficient conditions for stability, asymptotic stability, and so on.

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Опубликовано: 23 окт. 2023 г.

By using suitable Lyapunov functionals and LaSalle's invariance principle, we studied the global asymptotic stability of infection-free equilibrium and CTL ...

The stability of linear system can be determined by asymptotically stability criterion and Bounded-. Input-Bounded-Output (BIBO) stability criterion.

12 окт. 2021 г. · By using appropriate Lyapunov functions, the uninfected equilibrium point is proven to be globally asymptotically stable when the reproduction ...