关键词: 混合系统, 不变集, 李雅谱诺夫函数, 线性矩阵不等式

Abstract:

In order to solve the problem of existence of the invariant sets in hybrid systems, a class of hybrid system with perturbed disturbance is investigated. By proposing a common Lyapunov function, the existence of invariant set is proved. Moreover, by constructing a Lyapunov function, the existence is calculated based on the linear matrix inequality （LMI） method, the switch laws and sub-system domains of the hybrid system are obtained, and the do- main of the invariant set is further computed. A numerical example is finally presented to confirm the feasibility and effectiveness of the proposed method.

Key words: hybrid system, invariant set, Lyapunov function, linear matrix inequality