Stability Analysis Of Several Impulsive Systems

The stability analysis for impulsive systems is an important subject in the field ofhybrid systems. In this paper, we have considered the stability problems of differentforms of impulsive systems. The main contents of the thesis can be briefly described asfollows:1. We discuss theL2stability of a class of nonlinear reset systems and exponentialstability of a class of reset control systems with neutral type.L2stability criterion isobtained using Lyapunov function method, which provides a framework for the analysis ofexponential and input-output stability of nonlinear reset systems and is useful in thedevelopment of systematic reset controller design procedures. On the other hand, a sufficientcriterion for the exponential stability of reset control systems with neutral type is given byusing Lyapunov function method and the linear matrix inequality (LMI).2. We analyze the global exponential stability of a class of neutral-type impulsive systemwith time delay. The sufficient condition of global exponential stability is given, which isbased on the Lyapunov stability theory. Moreover, the problems of exponential stability ofother neutral-type impulsive systems with time-delay can be analyzed by means of this theory.Numerical example illustrates its effectiveness.3. We analyze the stability of a class of neutral delay switched systems. The problem ofstability for a class of switched neutral systems with discrete and distributed delay isinvestigated based on arbitrary switching rule. The sufficient condition is derived by usingLyapunov function technique. Numerical example illustrates its effectiveness.