Sliding Mode Control For Several Stochastic Systems With Markov Switching

In practical engineering systems, some kinds of reasons lead to variations insystem’s structure, parameter uncertain, time-delay, and nonlinear perturbations etc.Therefore, the applications of sliding mode control in these kinds of systems are ofpractical significance.The thesis is devoted to investigating sliding mode control(SMC) for threedifferent systems: Markovian switching singular systems with time-varying delaysand nonlinear perturbations; A class of nonlinear uncertain stochastic systems withinput nonlinearity and Markovian switching; Markovian switching neutral systemswith time-varying delays, Browinan motion and nonlinear perturbations.In Section Ⅱ, sliding mode control(SMC) for Markovian switching singularsystems with time-varying delays and delays and nonlinear perturbations isconsidered. The sliding mode controller is designed to guarantee the nonlinearsingular system is stochastically admissible and its trajectory can reach the slidingsurface in finite time. By using Lyapunov functional method, some criteria onstochastically admissible are established in the form of linear matrixinequalities(LMIs).In Section Ⅲ, sliding mode control for a class of nonlinear uncertainstochastic systems with input nonlinearity and Markovian switching is investigated.A non-fragile observer subjected to the transition rates of the modes is designed. Bysome specified matrices, the connections among the designed sliding surfacescorresponding to every mode are established. The state-estimation-based slidingmode control law is derived to guarantee the reachability of the sliding surface infinite time interval. The sufficient conditions on asymptotically stochastic stabilityof the error system and sliding mode dynamics with a given disturbance attenuationlevel are derived in terms of linear matrix inequalities (LMIs). Section Ⅳ is devoted to the investigation of sliding mode control(SMC) foruncertain neutral stochastic systems with Markovian jumping paramrters andtime-varying delays. The sliding mode control law is designed to guarantee thereachability of the sliding surface in a finite time interval. The sufficient conditionsfor asymptotically stochastic stability of sliding mode dynamics with a givendisturbance attenuation level are derived in terms of linear matrix inequalities(LMIs). Finally, an example is provided to illustrate the efficiency of the proposedmethod.