无限维混杂系统及其稳定性

该文基于半群理论对无限维的系统进行了建模,给出了用半群理论的无限维的混杂系统的模型,在此模型的基础上给出了其渐进稳定和一致有界的定义,并根据多Lyapunov方法等手段给出了几个无限维混杂系统在任意切换的情况下渐进稳定的条件。针对于无限维的线性切换系统,给出了具有有限个子系统的情况下的公共Lyapunov函数存在的条件,扩展了已有文献中的成果,最后还基于循环算子的定义和性质给出了一个等价的定理。

Hybrid System with Infinite Dimensions and Its Stability

This paper is concerned with the modeling of hybrid systems with infinite dimensions by semigroup theory,and by approaches such as multi-Lyapunov methods,several asymptotical stability criteria are given out based on special definitions of asymptotical stability and uniformly bounded on this particular hybrid system model.A specific theorem is proposed for the existence of common lyapunov function to the infinite dimensional switched systems with finite subsystems,which extends the current results,and then based on the definition and characteristic of the circular operator,one equivalent theorem is proposed concerning the existence of common Lyapunov function.