Control Design And Stability Analysis For Nonlinear Switched Systems Based On T-S Model

This thesis investigates the problem of stabilization and control design for classes of nonlinear switched systems with measurable or unmeasured states, fuzzy T-S model is used to identify the nonlinear switched systems, based on parallel distributed compensation(PDC) design scheme, by combining space partition strategy, Lyapunov function method and linear matrix inequalities(LMIs) theory, the control design and stability analysis of nonlinear switching system is studied. The detailed content of dissertation is as following:(1) For a class of switched systems with actuator saturation and time-varying delay,the fuzzy T-S model is used to identify the nonlinear switched systems, a switched state observer is designed to obtain the estimations of the unmeasured states, and the saturation nonlinearity is transformed into the convex combination in order to solve the problem of saturation. By using parallel distributed compensation(PDC) design scheme, a robust fuzzy output feedback control law is designed. Based on space partition strategy and Lyapunov function scheme, the signal switching law is constructed. The sufficient conditions of ensuring the switched fuzzy control system asymptotic stabilization are proposed and formulated in the form of linear matrix inequalities(LMIs). One numerical example and the mass-spring-damping system example are given to illustrate the effectiveness of the proposed control method.(2) For a class of switched systems with measurable states and actuator dead-zone, the fuzzy T-S model is used to identify the nonlinear switched systems, the dead-zone model is expressed as the linear input and nonlinear characteristics, and a robust fuzzy control law is developed to eliminate the effect of dead-zone nonlinearity. Based on single Lyapunov function method, the sufficient conditions of ensuring the switched fuzzy control system asymptotic stabilization and the switching law are proposed, The proposed control method can not only ensure the closed-loop system to be stable, but also guarantee the H-infinty performance index is reduced as small as possible. A numerical example is given to illustrate the effectiveness of the proposed control method.(3) For a class of switched systems with unmeasured states and actuator failures, an adaptive output feedback fault-tolerant control scheme is investigated. In the control design, the fault type considered in this study is the loss of actuator effectiveness, the fuzzy T-S model is used to identify the nonlinear switched systems, and a switched state observer is established for estimating the unmeasured states and the information of actuator faults. By using the online estimation of actuator faults, a new controller which composed of a normal controller and an adaptive controller is developed, in which the compensation control term is introduced in order to reduce the effect of actuator faults. By using the single Lyapunov function method, the switching law is constructed, and the sufficient conditions for ensuring the asymptotic stability of the switched fuzzy systems are proposed. The simulation example is given to illustrate the effectiveness of the proposed control method.(4) For a class of switched large-scale system with measurable states and actuator saturation, the fuzzy T-S model is used to identify the nonlinear switched systems, based on the state of ellipsoid domain constraints and by using H-matrices method, the control input constraints and saturation nonlinearity are analyzed. Under the PDC approach, a decentralized fuzzy controller is developed. The decentralized switching law and the stabilization sufficient conditions are proposed and proved based on the multiple Lyapunov function theory. It is proved that proposed control scheme can guarantee that whole closed-loop system is asymptotically stable. A numerical example is given to illustrate the effectiveness of the proposed control method.(5) For a class of switched nonlinear large-scale systems with immeasurable states and actuator dead-zone, a switched state observer is designed to estimate the unmeasured states, and the dead zone model is decomposed into two parts, which composed of input linear group and input nonlinear group, in order to overcome the effects of unknown dead zone. Under the theoretical framework of T-S model, an output feedback decentralized fuzzy controller is developed. The method of multiple Lyapunov function is used to analyze system and makes the system asymptotically stable under the switching strategy, by solving the LMIs, the sufficient conditions for asymptotic stability of the system is proposed. A numerical example is given to illustrate the effectiveness of the proposed control method.