Generalized H₂Control For Fuzzy Systems

Fuzzy control theory and fuzzy control technology have become one of the mainefective control methods to deal with the nonlinear systems, meanwhile, they also havebecome one of the main research topics of control community. Recently, fuzzy controltheory and fuzzy control technology have made greatly progress, and they have beensuccessfully applied to many felds, such as aeronautical space technologies, life science,social economic, and so on. The T-S fuzzy model is very important in the fuzzy controltheory. An advantage of a T-S fuzzy model is that, when it is applied to study the systemanalysis and controller design, one can frst represent a nonlinear system as a fuzzy model,and then study the problems of stability and controller design by using a systematicapproach. When uncertainties, mixed time delays and/or stochastic disturbance appearin a T-S fuzzy system, they may afect the system performance seriously, and even makethe system unstable. Hence, this dissertation is concerned with the generalized H₂controlproblems for T-S fuzzy linear systems, T-S fuzzy bilinear systems and T-S fuzzy large scalesystems, based on the previous studied, regarding new problems and using new researchmethods, some of the control problems for T-S fuzzy systems are solved.Since the common Lyapunov function stability theory has some conservatism in thefuzzy system analysis and control problems, the dissertation has given more relaxed sta-bility conditions by developing several new Lyapunov functions and controllers, and usestwo new techniques, namely the free-weighting matrix technique and relax LMI approachto reduce the conservatism in system design, further more, it can deal with generalizedH₂output feedback control problem efectively, we obtains the following research results:（1） Based on PQLF and Non-quadratic Lyapunov function, the problem of gener-alized H₂stabilization of discrete T-S fuzzy system with infnite-distribute delays havebeen studied. Some new less conservative sufcient conditions for generalized H₂stabi-lization are derived, and the corresponding piecewise non-fragile and memory controllerare obtained, respectively.（2） The stability of discrete nonlinear systems is concerned based on the T-S fuzzybilinear model. First, generalized H₂and robust generalized H₂stability of uncertainT-S fuzzy bilinear system with time-delay and distribution is studied by using PQLFto obtain some sufcient delay-dependent stabilization conditions for closed-loop systemsand present piecewise non-fragile controller design method; second, considering that theinformation of the system’s state and output are not enough to construct the controller, stabilization of T-S fuzzy bilinear system and T-S fuzzy bilinear system with infnity-distributed delays are discussed based on fuzzy bilinear observer control; last, an iterativealgorithm is got by making use of sequential linear programming matrix method （SLPMM）to derive a single-step LMI condition for fuzzy observer-based control design.（3） By considering stochastic perturbation commonly in T-S fuzzy bilinear system,we studied the mean-square stability and the generalized H₂mean-square stability ofT-S fuzzy bilinear stochastic system with mixed time-delays, respectively. By construct-ing new Lyapunov functions which are delay-dependent case with two class delays andconsidering the useful terms and using some free-weighting matrices, we derive someless constraint delay-dependent stabilization conditions of closed-loop T-S fuzzy bilinearstochastic system with time-delays and obtain the corresponding statics output feedbackcontroller.（4） we making stabilty analysis of discrete-time T-S fuzzy large-scale systems. First,combining with the properties of large-scale system and T-S fuzzy bilinear system, general-ized H₂and robust generalized H₂stability of discrete-time T-S fuzzy bilinear large-scalesystems is studied, based on decentralized control theory and SLPMM, the state feed-back controller design is presented in the form of LMI, to design the controller; secondly,generalized H₂and robust generalized H₂mean-square stability of T-S fuzzy large-scalestochastic systems with mixed delays are discussed and the decentralized negative statefeedback controller design method is presented.Several illustrative examples are provided to demonstrate the efectiveness of theproposed approaches in this paper.