Exponential Stability And Input-output Stability Analysis Of Time-delay Systems With The Interaction Effect Of Impulse And Delay

During the past few decades,due to the complex dynamic and wide application background of hybrid systems,the stability analysis of hybrid systems has received considerable attention.As a common class of hybrid systems,impulsive system,whose continuous behavior is interrupted by instantaneous state jumps,can provide a natural framework for mathematical modeling of many physical systems in real life,which is widely used in biology,cryptography,industrial robot control and other fields.In the meantime,time delay occurs on the system state or the derivative of state frequently,which is reflected as network induced delay and current transmission delay in reality.Therefore,it is of great theoretical significance and practical value to study the delay-dependent stability of impulsive time-delay systems.This thesis focuses on establishing low conservatism criteria of exponential stability and hybrid L2× l2-gain of impulsive time-delay systems and neutral timedelay systems by constructing novel Lyapunov functions/functionals which make full use of system characteristics.And both the linear and nonlinear systems are considered.The main results derived in this thesis are listed as follows:(1)The delay-dependent stability problem of a class of linear impulsive delay systems is studied.A novel impulse-timer-dependent Lyapunov functional is constructed based on the delay-partitioning framework,which depends on the partition on impulse intervals and also on impulse dynamics.By use of the new-type Lyapunov functional,combined with loopedfunctional method,Young inequality and extended Jensen's inequality,the exponential stability and finite hybrid L2×l2-gain analysis problems are studied.The new-type Lyapunov functional's structure ensures that at most one impulse instant happens in all delay subintervals,for purpose of reducing the influence on the stability analysis of the system caused by the interaction between impulse and time delay.Finally,by use of new integral inequalities based techniques,delay-dependent criteria for exponential stability and hybrid L2× l2-gain are established in terms of linear matrix inequalities.(2)The dwell-time dependent stability problem of a class of linear neutral-type time-delay systems with impulsive effects is studied.In the framework of descriptor system representation,a piecewise impulse-timerdependent Lyapunov functional is introduced to analyse the effects on stability of the system caused by state-delay and impulse-dwell-time.Compared with the previous research,the positive definiteness property of the Lyapunov functional within impulse interval is no longer necessary during stability analysis,which lowers the conservatism.In the meantime,NewtonLeibniz formula is used to handle the relationship among the augmented state variables.Then by use of linear matrix inequalities,criteria for exponential stability and hybrid L2× l2-gain are obtained.The efficiency of the theoretical result is shown by two numerical examples.(3)The Lp-stability problem of a class of nonlinear time-delay systems with delayed impulse and external disturbances is studied.By use of state augmentation method,the impulses-delayed system is modeled as an impulse-delay free system with switching impulses so that the technical difficulties caused by delayed impulses are circumvented.A novel timedependent Lyapunov function is constructed based on the switching structure of the augmented system.Combined with the Lyapunov-Razumikin method,sufficient conditions for exponential stability and Lp-stability are obtained,which characterize the relationship among the size of impulse-delays,the impulse intervals and the performance of Lp-gain.(4)The L2-stability problem of a class of nonlinear neutral-type timedelay systems with delayed impulse and external disturbances is studied.Similarly,the same modeling method of the previous chapter is used to deal with the delayed impulses.And a new-type time-dependent Lyapunov function is constructed to handle the delay on state as well as state-derivatives.The efficiency of the result is shown by a numerical example.Based on some relevant lemmas,the Lyapunov function combined with state derivative delayed term is transformed into the Lyapunov function combined with the state term during the stability analysis.