Sliding Mode Variable Structure Control For Several Uncertain Systems With Time-delay

Sliding mode variable structure control for time-delay systems is dynamic responsebased on the state space, which is infinite dimensional, highly nonlinear anddiscontinuous switching manifold. Stability and comprehensive analysis of this kindof problem is multiple difficult and complex. The actual dynamic system hasuncertainty, time-delay and nonlinearity. Therefore, the domestic and foreign scholarshave been interested in sliding mode variable structure control research for uncertaintime-delay systems. In this paper, sliding mode singular system history anddevelopment of control theory are introduced like adaptive variable structure control(AVSC) for uncertain singular systems with time-delay, uncertain delay systems anddiscrete singular systems, delay-dependent passive control for uncertain discretetime-delay singular system, sliding mode control(SMC) for a class of uncertainstochastic Markovian jump systems with time-delay and the latest researchdevelopments are reviewed in this area. Several problems are put forward to bestudied.In chapter1，the development of singular VSC theory is reviewed, some historysurvey and research at home and abroad are introduced for the singular systems,stochastic systems, delay systems and uncertain systems. The contents and methods ofthe paper are shown.In chapter2, AVSC problems of linear systems with time-varying multi-delays andmismatching uncertainties are discussed. Firstly, the state equation of the system isconverted into a canonical form, can be very intuitive to see that mismatchingtime-varying uncertainty and time-delay. A new adaptive variable structure controlleris given by Lyapunov stability theory and the corresponding reasonable assumptions. The full invariance of sliding mode with time-varying multi-delays and mismatchinguncertainties is proved in the circumstances sliding surface coefficient matrix tosatisfy certain matching conditions. The control strategy ensures that the closed-loopsystem is globally stable. Simulation results further show that the given controlstrategy of this paper is feasible and effective.In chapter3, AVSC problems of singular linear time-invariant delay systems withuncertainties are discussed. A new adaptive variable structure controller is given byLyapunov stability theory and the corresponding reasonable assumptions. Theinvariance of sliding mode is proved in the circumstances of the external disturbanceand parameter perturbation with matching conditions. Through memory andmemoryless of the linear state feedback, the control strategy ensure that systemreaches sliding mode in finite time and the closed-loop system is global asymptoticstable. Simulation results further show that the given control strategy of this paper isfeasible and effective.In chapter4, the problem of designing sliding mode variable structure control (VSC)for uncertain system is considered. The two new concepts of ideal reaching law andadaptive reaching law are proposed and two types of approaches of VSC based onreaching law are designed. The similarities and differences of designing sliding modeVSC are analyzed. Sliding mode variable structure controller system designed byapplying two types of reaching laws not only can reach the region of the switchingsurface in finite time and the stability of system origin can be guaranteed, but also thesystem chattering is decreased effectively and enhances the dynamic quality of thecontrol system. Simulation results illustrate the feasibility of the proposed approach ofthis paper.In chapter5, synthesis problem of SMC for mismatched discrete singular systems(DSS) with internal parameter perturbation and external disturbance is considered.Dynamic switching function with last step state vector is given to guarantee thestability of the control system in the switching band. Discrete singular reaching law with dynamic disturbance compensator is designed to eliminate the restriction of thesystem uncertainties is bounded and the satisfaction of matching conditions comparedwith conventional SMC and provides essential condition of quasi-sliding mode whichcan cross the switching plane step by step. Discrete singular sliding mode controller isdesigned by applying the reaching law, which can guarantee the system to reach theswitching plane in finite time, decrease the system chattering effectively and enhancethe dynamic quality of the system. For a class of unmatched uncertain discretesingular systems, the quasi SMC is also gives a new discrete singular reaching law,this rate reaching law reduced quasi sliding mode bandwidth of the system, furtherweakening chattering. A numerical example is used to illustrate the feasibility andeffectiveness of this method of this paper.Chapter6is concerned with SMC for a class of uncertain stochastic Markovian jumpsystems with time-delay. The jumping parameters considered here are generated froma continuous-time discrete-state homogeneous Markov process, which are governedby a Markov process with discrete and finite state space. A concept of thesubordinated reachability for the sliding motion is first introduced to approachapproximately the specified sliding surface. The sliding mode controller is thenproposed to ensure that the sliding motion is subordinated reachable. Furthermore, asufficient condition is given such that the sliding motion is mean-square asymptoticalstability. Finally, a simulation example is presented to demonstrate the effectivenessof the obtained results.Chapter7investigates delay-dependent robust passive analysis and control foruncertain discrete singular system with multiple time-delays. Delay-dependent robustpassive condition in terms of linear matrix inequalities (LMI) for the discrete singularsystems is obtained by employing Lyapunov-Krasovskii approach and free weightingmatrix technique. Based on this condition, a delay-dependent robust passive controlleris presented which guarantees the resultant closed-loop system to be regular, casual, stable and robust passive. A numerical example is provided to demonstrate theeffectiveness of the method.The last chapter summarizes the main work, gives the main innovation, finally putforward some issues to be researched.