Research On Two Stability Problems Of Discrete Pulse Switched Time-delay Systems

The problem of stability for dynamical systems is always the main study of systems.This paper mainly employs the method of subsequence to study two kinds of stabilities of discretetime impulsive switched delay systems by constructing the Lyapunov functions.The paper is mainly divided into two parts,the first part is to present the study of input-to-state stability for a class of discrete time-delay systems with switching and impulsive signals,the second part is to analyse the almost sure stability for a class of discrete-time nonlinear Markovian jump delayed systems with impulsive signals.The main contents of the paper are as follows:The second chapter mainly investigates the input-to-state stability(ISS)for a class of discrete time-delay systems with switching and impulsive signals.By the Lyapunov-Krasovskii techniques,a dwell-time bound and a delay bound are clearly presented to contribute to the ISS for discrete time-delay systems.A significant subsequence method of the switching and impulsive sequence would be firstly applied to study the ISS of discrete systems.Based on this method,some new conditions guaranteeing ISS are presented.Compared with the existing results on related problems,the obtained stability criteria are less conservative as these conditions only require the specially designed Lyapunov functions to be nonincreasing along each of the specially defined subsequences of the switching and impulsive times.The third chapter investigates the almost sure stability for a class of discrete-time nonlinear Markovian jump delayed systems with impulsive signals by using Lyapunov functions,and the subsequence method.It is pointed out that,even if all the Markov jump subsystems are not almost sure stable in the case of no impulses,impulses can still be devoted to achieving the almost sure stability of the system in the specially designed interval,i.e.,the impulsive switchings and Markov jumps satisfy a dwell time upper bound condition.In addition,these almost sure stability results can also be applied to the systems with arbitrary large time-delays as well.Conversely,when all the Markov jump dynamics are almost sure stable in the absence of impulses,the system can still maintain the properties of almost sure stability if the impulse parameters remain in a limited range.Finally,this paper takes also the combination of the first and the second case into consideration.