Stability And L₂-Gain Analysis Of Impulsive Switched Systems

As a typical hybrid dynamic system,the switched systems have been applied in many fields.Affected by the discrete dynamic behavior at the switching instants and some unknown irresistible factors,the system states may jump instantaneously and result in impulse phenomena,which will lead to complex dynamic behavior.Therefore,the study of the impulsive switched systems has practical significance.In recent years,the research on the dynamic performance of the impulsive switched systems has attracted extensive attention of scholars.This thesis mainly studies the stability and L₂-gain performance of the impulsive switched systems with time delays,in which the impulsive switching signals are in an incommensurate phenomenon,that is,the impulse instants are not constrained by the switching instants.It mainly includes the following contents:Firstly,the research background and significance,some necessary definitions and lemmas,and the main work of this thesis are introduced.Secondly,it studies the stability and L₂-gain performance of the linear impulsive switched systems with time delays,where two types of impulses effects are considered.On the one hand,based on the Lyapunov-Razumikhin（L-R）method,su cient criteria for the exponential stability and L₂-gain performance of the unstable impulses coupled stable subsystems are obtained.On the other hand,by proving a class of impulsive switched differential inequalities,su cient conditions for the exponential stability and L₂-gain performance of the stable impulses coupled unstable subsystems are established.In addition,using the average dwell time（ADT）and the average impulsive interval（AII）conditions,the design methods of the incommensurate impulsive switching signals under the unstable impulses are given.Correspondingly,for the stable impulses,the impulsive switching signals can be designed with the ADT and the reverse AII conditions.Furthermore,combining some numerical examples,the feasibility of the above theoretical results is illustrated.Thirdly,it considers the stability and L₂-gain performance of the linear impulsive switched systems with time delays under hybrid impulses,that is,unstable impulses and stable impulses can coexist simultaneously.In the framework of the L-R method,su cient criteria for exponential stability and L₂-gain performance of the systems under hybrid impulses are presented.Based on the mode-dependent average dwell time（MDADT）and the mode-dependent average impulsive interval（MDAII）conditions,the incommensurate impulsive switching signals can be designed.The validity of the results is verified by some numerical simulations.