The Research On Sliding Mode Control Of Semi-markovian Jumping Systems With Time-delays

Semi-Markovian jumping systems can be used to describe various systems with sudden changes in structure and parameters.The systems is widely used in communication networks,industrial manufacturing,aerospace and other systems.On the other hand,the existence of time delay usually makes the analysis and synthesis of the system more complex and difficult,and also leads to the systems performance deterioration,even instability.In addition,in the actual systems modeling process,uncertainties and external disturbances will inevitably be introduced into the systems with the control input,and sliding mode control has significant advantages in the research of related issues.Therefore,it is of great significance to study the stability and stabilization of semi-Markovian jumping systems with time-delays by using sliding mode control.In this thesis,we focus on the stability and stabilization of semi-Markovian jumping systems with time-delays through inequality constraint techniques and sliding mode control.The details are as follows:(1)For the sliding mode controller design problem of continuously uncertain semiMarkovian jumping systems with time-varying delays.Firstly,by studying the dynamic characteristics of the systems,combined with the sliding mode surface,a singular system is established to describe the holonomic dynamics of the sliding mode.Then,building an appropriate Lyapunov functional by taking into account more information about time delay,a sufficient condition that guarantees the existence of sliding mode surface and the stochastic stability of sliding mode dynamics is given.Based on this,a sliding mode controller is designed to make the closed-loop system finally converge to the sliding mode surface.Finally,a numerical example is given to show the correctness and effectiveness of the method.(2)For the observer-based integral sliding mode control problem of continuously uncertain neutral semi-Markovian jumping systems with time-varying delays.Firstly,by studying the dynamic characteristics of the original system,a state observer is designed to estimate the systems state,and the error systems of the original system and the state observer is obtained.And an integral sliding surface is designed in the state estimation space to establish a system describing the complete dynamics of sliding mode.Then,building an appropriate stochastic Lyapunov-Krasovskii functional by taking into account more information about time-varying delays,a novel sufficient condition is established for the robustly stochastic stability of the overall system made up of the error system and the sliding mode dynamics system.Based on this,an integral sliding mode control law is devised to ensure the reachability of the integral sliding surface in a finite time.Finally,two numerical examples explain the correctness and effectiveness of the results obtained.(3)For the stochastic finite-time boundedness problem using the sliding mode control method for uncertain neutral semi-Markovian jumping systems with time delays under the multi-rate sampled-data event-triggered strategy.A key issue is how to combine the sliding mode control and the multi-rate sampled-data event-triggered control to achieve the stochastic finite-time boundedness of the closed-loop system.To this end,firstly,based on the multi-rate sampled data,a new event-triggered scheme is introduced for the first time.Then,the sliding surface and the event-triggered scheme are integrated to obtain the closed-loop system,by building an appropriate two-sided looped-functional,the existing condition of the sliding surface and the stochastic finite-time boundedness condition of the closed-loop system are presented.Furthermore,an event-triggered sliding mode control law is devised to ensure the reachability of the sliding surface in finite time.Finally,a numerical example explains the feasibility and effectiveness of the results obtained.