Study On Low Conservatism Control And Stability Analysis Method For T-S Fuzzy Systems

T-S fuzzy model describes the nonlinear system as a combination of a group of linear subsystems through membership functions,and transforms the nonlinear control problem into the linear control issues.Thus,a large amount of mature linear system theories can be adopted and a systematic way to deal with the control problem of nonlinear system is provided.Based on the T-S fuzzy model,the stability analysis and control synthesis problems of fuzzy systems are investigated in this paper:To solve the stabilization control problem of T-S fuzzy system,the premise variable space is divided into several sub-domains in premise variablemembership coordinate system.Based on piecewise linear approximation method for membership function,a local controller is designed for each sub-domain.Quadratic Lyapunov function and piecewise Lyapunov function are used to analyze the stability of the closed-loop system,and the problem of asymptotic stability of the closed-loop system is transformed into the feasibility problem of solving Linear Matrix Inequality(LMI).Then,a less conservative local fuzzy controller is creatively designed,and a series of LMI conditions are obtained by using fuzzy Lyapunov function.Compared with the classical control method,the two controllers designed in this paper do not need to choose the membership function artificially,which leads to less conservative.The local fuzzy controller method is better,for that matter.Finally,the efficiency of the proposed method is verified by simulation examples.To solve the problem of stability analysis of open-and closed-loop T-S fuzzy systems,an equilibrium point enveloping method is proposed.The premise variable space is divided to obtain a series of subdomains,and the maximum and minimum of membership function are calculated in each subdomain.After coordinate transformation,the vertices of convex polygon that can envelop the original trajectory of membership function are obtained in membership function space.At the same time,the stability analysis problem can be transformed into the LMI conditions at the vertex of convex polyhedron,but the complexity of this method is multiplied when too many fuzzy rules exist.Therefore,the piecewise linear approximation method is introduced,and the endpoint obtained by adding and subtracting the approximation error term from the membership function estimation term is mapping to the vertex of a convex polyhedron,which can also envelope the trajectory of the original membership function curve.Compared with previous methods,the two methods are less conservative.In view of the existence of disturbance,the robust stability condition can be obtained by using performance index and the method based on plane and cube envelope.Finally,the efficiency of the proposed method is verified by simulation.