广义切换系统的脉冲性质及其稳定性

Impulsiveproperty of switched singular systems and its stability

广义切换系统是一类重要的混杂动态系统,有着广泛的实际背景。研究了广义切换系统由于非一致的初始条件引起的状态跳变问题,同时讨论了一致初始条件和非一致初始条件下广义切换系统解之间的关系。广义切换系统的每个子系统具有不同的代数约束条件,这类广义切换系统的特点是在每一个切换时刻都有脉冲影响作用于系统。将标称切换系统的多李雅普诺夫方法应用于该类带有脉冲作用的广义切换系统,对每一个子系统,引入类李亚普诺夫函数(Lyapunov-like Function),基于类李亚普诺夫函数和多李亚普诺夫函数方法,得到了系统稳定的充分条件。

Switched singular system is one of the important hybrid dynamical systems. In this paper the problem of state jumps due to inconsistent initial conditions is addressed for impulsive and switched singular systems. The relationship between the solution with inconsistent initial condition and the one with consistent initial condition is discussed as well. The switched singular systems of each subsystem with different algebraic constrain conditions is modeled by switched singular systems with impulsive effects on switching instants. Multiple Lyapunov function approach for normal switched systems is extended to the impulsive and switched singular systems. For each subsystem,the Lyapunov-like function is introduced and the sufficient condition for the systems to be stable is given based on the Lyapunov-like function and Multiple Lyapunov function.