Study On The Dwell Time Dependent Stability And Stabilization Of Linear Impulse System

Impulsive system is a hybrid dynamic system.The state trajectory of the impulsive system is continuous between two adjacent impulsive instants,but it jumps at the impulsive instant.Because of this characteristic,impulsive systems have been widely used in forestry,electrical engineering,epidemiology,networked control systems and sampled-data systems.Therefore,it is very important to study the relationship between the stability of linear impulsive systems and the dwell-time,that is,the dwell-time dependent stability,and the stabilization problem.At the same time,there must be system uncertainty in practical engineering,so it is also a valuable problem to study the robust stability of uncertain impulsive systems.In this paper,the dwell-time dependent stability of linear impulsive systems is studied.The relationship between stability and dwell-time is studied by Lyapunov-like functional method,and the dwell-time dependent stability criterion is derived.Then the stability criterion is extended to the convex polygon uncertain impulsive systems and the dwell-time dependent robust stability results are obtained.Finally,the stability criterion is modified to fit the state feedback control,and the new stability results are given.Based on the stability results,a state feedback controller is designed to make the closed-loop system asymptotically stable.Numerical simulation results show that the proposed control method is effective and feasible,and the stability results obtained are less conservative than before.The details are as follows:The chapter 1 introduces the research significance and background of linear impulsive systems,reviews the research process,points out the existing problems,and gives the linear impulsive system and convex polygon parameter uncertainty impulsive system,as well as the state feedback closed-loop system model.In chapter 2,the definitions,lemmas,theorems and other basic theoretical knowledge are introduced to study the stability and stabilization of linear impulsive systems,as well as the treatment of linear matrix inequalities.These preparatory knowledge provide the method and theoretical basis for the following chapters.In chapter 3,the dwell-time stability of impulsive systems is studied by Lyapunov-like functional method.A Lyapunov-like functional is constructed by introducing multiple integrals of system states,multiple integrals of state derivatives,and cross terms between states and impulsive states.The Lyapunov-like functional of this class requires neither global positive definite nor continuity,and is more general than the existing functional.In order to estimate the derivative of this Lyapunov-like functional,the integral inequalities of higher order are used,especially the integral equation of impulsive system is developed,and a less conservative upper bound is obtained.According to Lyapunov-like functional method,a new dwell-time dependent stability criterions are derived,including the maximum and minimum dwell-time dependent stability results.Then,the stability criterions are extended to the convex polygon parameter uncertainty,and the robust stability results are derived.Finally,the numerical simulation results show that: the stability results obtained are less conservative than before.In chapter 4,the stabilization of linear impulsive systems is studied.A new stability theorem is obtained by modifying the stability criterion for state feedback.This theorem is applied to the state feedback system,and the corresponding stability conditions are transformed by contract transformation,variable substitution,etc.Then,the design theorem of state feedback stabilization controller for impulsive system is obtained.This theorem transforms the state feedback stabilization problem of impulsive system into the feasibility problem of LMI and gives the design method and steps of the controller.Finally,the controller design method is proved to be feasible by numerical simulation.The fifth chapter is the summary of the full text,and points out the problems to be studied in the future.