Forward and Converse Lyapunov Theorems for Discrete Dynamical Systems
| Autor: | Martin T. Hagan, Reza Jafari, Anthony Kable |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Lyapunov function
Mathematics::Dynamical Systems Dynamical systems theory Mathematical analysis Lyapunov optimization Lyapunov exponent Computer Science Applications Nonlinear Sciences::Chaotic Dynamics symbols.namesake Control and Systems Engineering Stability theory symbols Applied mathematics Lyapunov equation Electrical and Electronic Engineering Lyapunov redesign Mathematics Control-Lyapunov function |
| Zdroj: | IEEE Transactions on Automatic Control. 59:2496-2501 |
| ISSN: | 1558-2523 0018-9286 |
| DOI: | 10.1109/tac.2014.2304174 |
| Popis: | This technical note addresses the stability analysis of nonlinear dynamic systems. Three main contributions are made. First, we show that the standard assumption of a continuous Lyapunov function can be (and in some cases must be) relaxed. We introduce the concept of the `weak' Lyapunov function, which requires that an annulus condition be satisfied. We believe that this annulus condition is a more natural construct, because it is precisely what is needed to make the forward Lyapunov theorem true. Second, we provide an example of a nonlinear system with stable equilibrium point that cannot be shown to be stable with a continuous Lyapunov function. Finally, we demonstrate a simpler and less restrictive proof of the converse Lyapunov theorem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|