Stability Theory for Hybrid Dynamical Systems
This entry provides a short introduction to modeling of hybrid dynamical systems and then focuses on stability theory for these systems. It provides definitions of asymptotic stability, basin of attraction, and uniform asymptotic stability for a compact set. It points out mild assumptions under which different characterizations of asymptotic stability are equivalent, as well as when an asymptotically stable compact set exists. It also summarizes necessary and sufficient conditions for asymptotic stability in terms of Lyapunov functions.
KeywordsHybrid system Asymptotic stability Basin of attraction Lyapunov function
- More information about stability theory for hybrid dynamical systems, and related systems, can be found in selected books and journal papers from the stability and control literature.Google Scholar
- Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control 43:1679–1684Google Scholar
- Michel AN, Hou L, Liu D (2008) Stability of dynamical systems: continuous, discontinuous, and discrete systems. Birkhauser, BostonGoogle Scholar