A Class Of Hybrid Systems - Switching System Of Qualitative Stability Analysis

Hybrid system is a combination of discrete and continuous dynamical systems. These systems arise as models for phenomena, which cannot be described by exclusively continuous, or exclusively discrete processes. There are many perfect results on the stability of switching systems.This paper deals with the problem of stabilization of switched systems with time delays, and focuses on the stabilization of switched systems with discrete time delay and distributed time delay. It makes the existing results more perfect.The paper is organized as follows:1. This paper deals with the problem of a type of linear switching systems with discrete and continuous time delay. By constructing Lyapunov functional under a condition on the time delay, we show it stabilizes the system for sufficiently small delays.2. In this paper, we study stability and L₂ -gain for a class of switched systems with discrete time delays and distributed time delays. Sufficient conditions for exponential stability and weighted L₂ -gain are developed. These conditions are delay-dependent and are shown in the form of linear matrix inequalities. The state decay estimate is given. Several examples illustrate the effectiveness of the proposed method.3. In this paper, we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay-difference system-discrete time switched systems, and delay-independent robust stability and stabilization of it. We mainly used a discrete version of the second Lyapunov method.4. This article gives a novel criterion for the asymptotic stabilization of the zero solutions of a class of switched systems with delays in control input. By constructing Lyapunov functional, we obtained the criterion which is expressed in terms of matrix inequalities. The results are more advanced than the references. Numerical examples are presented to illustrate the effectiveness of the theoretical results.