Stability And Stabilization Of Edge-dependent Pulse-switched Systems

The research of impulsive switching systems,which not only contains the characteristics of switching systems,but also holds the features of impulsive systems,has always caught people's attention.This paper mainly studies the problem of stability and stabilization of the impulsive switching system.Moreover,sufficient conditions are obtained to stabilize the system.In this paper,the stability analysis and synthesis of asynchronous switching systems,stochastic impulsive switching systems and time-delay impulsive hybrid systems are discussed by constructing multiple Lyapunov functions and combining the characteristics of the edge-dependent method.The main researches are as following contents:1)Stabilization and stability of the impulsive switching system with asynchronous switching mechanismThe main objective of this part is to explore the stabilization and stability of a family of impul-sive switching system under asynchronous switching.It allows that the points of impulses may be inappropriate to switches,and the number of impulses may be greater than one on any switching interval.Besides,we construct a new Lyapunov-like function,and the difference is that it can be discontinuous at discrete points compared with ancient forms,of which discrete points including impulsive points,switching moments and the instants when system modes and controller modes are matched.By adopting the edge-dependent average dwell time approach,the upper bound of average dwell time of each mode can be obtained in order to ensure the stability of the system.Moreover,the state feedback switching controller and the gain matrix of the controller can be ac-quired through utilizing the linear matrix inequalities.At the end of this chapter,some numerical examples and two simulation results are given to prove the validity of our main results.2)Stochastic input-to-state stability of the nonlinear switching systems with a single jump map or multiple jump mapsThe linear impulsive switching system is extended to the nonlinear random system,and the definition of the stability of the stochastic input-to-state is given.The impulse satisfies the Poisson distribution,which is divided into single jump map and multiple jump maps.Furthermore,aiming at the stability problem of random impulsive switching systems,sufficient conditions are obtained to guarantee the system to be stable by using Markov inequality,mathematical expectation and probability.The analysis of the conditions shows that stability can be achieved under whether single jump map or multiple jump maps.3)Input-to-state stability of hybrid time-delay systemsThe part inspects the input-to-state stability nature of hybrid time-delay systems.The differ-ence from the general time-delay system is that there may be delay at the impulsive or switching points.A novel concept of named admissible edge-dependent average impulsive interval is pro-posed for the first time,based on the concept of admissible edge-dependent average dwell time.According to Lyapunov-Krasovskii functionals,a relationship among average dwell time,average impulsive interval,decay rate of function and delay bound is established.Compared with other papers,our results extend results of other papers and have less conservatism and limitation.For example,its delay bound is not smaller than dwell bound,and allows the delay to take place at impulsive moments,etc.Finally,two numerical examples and two simulation results are given to prove the effectiveness of our main results.