An invariance principle for nonlinear hybrid and impulsive dynamical systems
- 作者：Chellaboina ; VijaySekhar ; Bhat ; Sanjay P. ; Haddad ; Wassim M.
- 关键词：Left-continuous dynamical systems ; Hybrid systems ; Impulsive dynamical systems ; Discontinuous flows ; Positive limit sets ; Invariant set theorems ; Stability theorems ; Lyapunov functions
- 刊名：Nonlinear Analysis
- 出版年：2003
- 期刊代码：43_0362546x
- 类别：mt
- 出版时间：May, 2003
- 卷：53
- 期：3-4
- 页码：527-550
- 文件大小：290 K
摘要
In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. Specifically, we show that left-continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.