A Sum-of-Squares Approach to the Analysis of Zeno Stability in Polynomial Hybrid Systems
| Autor: | Matthew M. Peet, Chaitanya Murti |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Lyapunov function
Dynamical systems theory Lyapunov exponent symbols.namesake Exponential stability Control theory Optimization and Control (math.OC) Hybrid system symbols FOS: Mathematics Applied mathematics Lyapunov equation Lyapunov redesign Zeno's paradoxes Mathematics - Optimization and Control Mathematics |
| Zdroj: | ECC |
| DOI: | 10.48550/arxiv.1310.2701 |
| Popis: | Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided. |
| Databáze: | OpenAIRE |
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