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Stability And Sliding Mode Control For Stochastic Singular (Neutral-Type) Systems

Posted on:2016-08-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:J JieFull Text:PDF
GTID:1108330473456381Subject:Detection and processing of marine information
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More uncertainties and external disturbance noise could be considered in the stochastic system, especially in the Markovian jumping system. The Stochastic system is greatly concerned and studied by its more accurate descriptions for the complexity of practical models. Sliding mode control is considered to be an important branch in the domain of the control theory. The features of the sliding mode control is claimed to result in fast response, well reduced-order model, high precision regulation, strong robustness to variation in parameter perturbations and external disturbances. Thus, the problems of stability and sliding mode control for singular or neutral-type Markovian jumping systems should be researched for their application background and important theoretical value.From the generally uncertain transition rate matrix considered as one of the innovative points, the stochastic stability analysis, state-feedback control, integral quantized control, sliding mode control, observer design based on sliding mode control and anti-windup H∞ control for actuator saturation of singular Markovian jumping systems (SMJSs) are considered as main purpose of this paper. In addition, mean-square exponential stability analysis, sliding mode control and observer design based on sliding mode control for neutral-type Markoivan jumping systems (NMJSs) are also considered. The research methods and contents of this dissertation are summarized as follows.(1) Utilizing the method of Lyapunov stability and the theory of matrix inequalities, three cases are discussed by the definition of the generally uncertain transition rate matrix. The criterion on the regularity and stochastic stability for SMJSs are obtained. Moreover, a sufficient condition of stochastic admissibility for a special class of SMJSs is extended by discussing three cases. The toolbox of Matlab is utilized, and a simulation example is given to illustrate the feasibility of above results.(2) By the existing lemma about the stochastic admissibility for SMJSs, a linear state-feedback controller is established, and the selection method for the state-feedback gain matrix is given. By the definition of the generally uncertain transition rate matrix, a sufficient condition is obtained for the stochastic admissibility of the closed-loop dynamic systems in three cases. The toolbox of Matlab is utilized, and a simulation example is given to illustrate the effectiveness of the design strategy for the linear state-feedback controller.(3) An integral quantizer is introduced by the theory of the linear operator, and the problem of the integer-quantizer control for uncertain SMJSs with the generally uncertain transition rate matrix is discussed. A state-feedback controller is designed with nonlinear part and linear part. Using Lyapunov stability method, a sufficient condition for the stochastic stability of closed-loop dynamic systems is obtained in three cases. The toolbox of Matlab is utilized, and a simulation example is shown to illustrate the rationality of the designed integer-quantizer is testified.(4) By the method of the sliding mode control, the problem of the stochastic robust asymptotic stability for SMJSs and the design strategy of the observer for stochastic singular uncertain systems with time-delays are investigated, respectively. For the reachability of the sliding mode, the appropriate sliding mode function and sliding mode controller are established such that trajectories of the system state do the stable sliding motion. By the toolbox of Matlab, a simulation example is shown to illustrate the effectiveness of the sliding mode controller or the observer based on the sliding mode control.(5) According to the strategy of dynamic output stabilization compensator, the anti-windup H∞ control for SMJSs with the generally uncertain transition rate matrix and actuator saturation is studied. By Dynkins formula and Ito formula, a sufficient condition for the H∞ stochastic stability of closed-loop dynamic systems is resulted. By the toolbox of Matlab, a simulation example is given to illustrate the rationality of the designed anti-windup compensator.(6) By Newton-Lebniz formula and It o formula, a new type of Lyapunov-Krasovskii functional is established, and a sufficient condition for the mean-square exponential stability of stochastic uncertain NMJSs is resulted. By the toolbox of Matlab, a simulation example is given to illustrate the feasibility of the proposed results.(7) The method of the sliding mode control is utilized, and the H∞ control and the non-fragile observer design for NMJSs are investigated. Then the sliding mode functional and the sliding mode controller are established, and a sufficient condition for the H∞ stochastic stability of the closed-loop dynamic systems based on the sliding mode control is obtained. By the toolbox of Matlab, a simulation example is shown to illustrate the feasibility of the proposed results.
Keywords/Search Tags:Markovian jumping system, generally uncertain transition rate matrix, sliding mode control, observer based on the sliding mode control, integer-quantizer control
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