Stability Analysis And Controller Design For Several Classes Of T-S Fuzzy Systems

Compared with classical control systems,fuzzy control can be easy to realize effectively human control strategies and experience,and achieve better control performance in the ab-sence of the accurate mathematic model for the control systems.Meanwhile,they have been successfully applied to many fields,such as aeronautical space technologies,life science,social economic and so on.Based on switching fuzzy model,Lyapunov stability theory,stochastic theory,H_?theory,generalized H₂ theory,matrix theory and so on,the focus of this thesis is to establish novel methodologies for stability analysis and control for several classes of T-S fuzzy systems.The main research contents of the thesis are as follows:1.Based on switching fuzzy model and piecewise Lyapunov functions,the problems of stability analysis and controller design for discrete-time T-S fuzzy systems with time delays have been studied.Some new less conservative sufficient conditions for H_?stabilization are derived.To reduce the stabilization criterion further,the interactions among the fuzzy subsystems are considered by using incidence matrix.In addition,incidence matrix is not required to be symmetric.2.H_?fuzzy filter design for two classes of discrete-time T-S fuzzy systems with time-delay is investigated.Firstly,we present a non-fragile H_?filter design method and give the design results in terms of LMIs.The main feature is the use of piecewise Lyapunov func-tionals which can reduce the conservatism arisen from the common Lyapunov functional approach.Secondly,we consider H_?switching fuzzy filter design in the stochastic case.Some new delay-dependent design results are established to ensure that the filter error sys-tem is stochastic stable with guaranteed H_?performance index.The main technique is the use of free-weighting matrix and matrix decoupling method.All sufficient conditions can be expressed in terms of LMIs and therefore are numerically tractable.3.We consider the H_?fuzzy static output feedback controller design for a general discrete-time T-S fuzzy stochastic systems with distributed time-varying delays.To achieve our purpose,we adopt the free-weighting matrix method,piecewise Lyapunov functions,and the matrix decoupling technique.Some drawbacks existing in the previous papers such as matrix equalities constraint,coordinate transformation,the same output matrices,diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated.4.By utilizing improved matrix decoupling technique,passivity theory and stochastic Lyapunov-Krasovskii functional,some new sufficient conditions in terms of resilient adap-tive controller are given such that the corresponding closed-loop It?o-type Markovian switch-ing stochastic system is almost surely asymptotically stable and robustly passive in the sense of expectation.5.Based on T-S fuzzy model,the consensus tracking problem is discussed for a class of nonlinear multi-agent systems with directed graph and time-varying topology.By using only the agent dynamics and the relative states of neighboring agents.the proposed distributed fuzzy adaptive control protocols guarantees that all estimation errors are bounded,and the tracking error remains in a neighborhood of the origin.Finally,the conclusion and future work are presented.