Robust Sliding Mode Control For Several Classes Of Discrete Uncertain Stochastic Singular Systems

It is well known that the singular systems have received extensive research attentions due to their distinct advantages of describing more performance characteristics than the normal system modelling ways.Generally speaking,the investigations on the synthesis problems of singular systems are relatively complicated in comparison with the normal systems owing to the fact that the resultant closed-loop systems are expected to satisfy stability,regularity as well as causality simultaneously.As one of the most effective robust control techniques,the sliding mode control(SMC)has been extensively applied in plenty of practical engineering systems due to its distinct strengths of strong robustness against parameter changes and external disturbances.In addition,some factors could cause deteriorated performance of the system,such as the phenomena of time-delays and data packet losses during transmission information via the network.Therefore,it is of great research significance on how to reduce the above unfavorable effects onto the control system performance and design a valid control mechanism.In this thesis,we intend to consider several classes of discrete stochastic uncertain singular systems and put forward some new robust SMC schemes.The main investigation contents are summarized as follows:Firstly,the adaptive SMC problem is discussed for a class of discrete singular systems subject to time-varying delays and randomly occurring uncertainty,where the uncertain occurrence probability case and the nonlinear disturbance are addressed.A proper discrete switching function is designed and the corresponding sliding mode dynamics is obtained.Furthermore,some sufficient criteria via the free weighting matrices idea are obtained to ensure the admissibility of the resultant sliding motion by introducing new Lyapunov-Krasovskii functional.In particular,a robust adaptive sliding mode control law is constructed,which is capable of ensuring the reachability of the pre-specified sliding surface.Based on above results,we further address the problem of robust adaptive SMC for discrete singular systems subject to randomly occurring mixed time-delays under uncertain occurrence probabilities.Here,the mixed time delays are considered,which are comprised of both the discrete interval delays and infinite distributed delays.Accordingly,a new robust adaptive SMC method is proposed based on the Lyapunov stability theory.Finally,the feasibility of the proposed robust adaptive SMC approach is illustrated by the numerical simulations.Secondly,the finite-time SMC issue is studied for a class of discrete-time singular Markov jump systems subject to data packet losses via the delay-fractioning approach.A random variable obeying the Bernoulli distribution is firstly used to depict the stochastic phenomenon of data packet losses.Based on the probability information of data packet losses and the compensation scheme,an appropriate sliding surface function is constructed,and the corresponding sliding mode dynamics is given.Next,sufficient conditions are obtained to ensure the singular stochastic finite-time boundedness(SSFTB)of sliding motion in view of delay-fractioning approach.Furthermore,a new SMC mechanism is proposed properly to compensate the effects induced by data packet losses,which ensures that the system states are driven onto a band of the specified sliding surface.Finally,the effectiveness of the proposed SMC approach is tested by numerical simulation.Thirdly,the robust finite-time H_?control problem is investigated for discrete-time singular Markov jump systems with partially known transition probabilities subject to randomly varying actuator faults(RVAFs)under uncertain occurrence probabilities via the SMC scheme.A set of random variable obeying the Bernoulli distribution is firstly utilized to describe the stochastic phenomenon of RVAFs.Based on the current state information,a novel sliding surface function is designed.Furthermore,new certain criteria are given for SSFTB of the sliding motion with prescribed H_?performance via Lyapunov stability theory and inequality processing method.Subsequently,a new SMC law is synthesized to compensate the effects induced by RVAFs,which guarantees that the system states are driven onto a band of the pre-designed sliding surface.Finally,the feasibility of newly proposed SMC strategy is illustrated by a numerical simulation.