Robust H_? Controller Design Under Imperfect Premise Matching For T-S Time-Delay Fuzzy Systems

The fuzzy model approach has been recognized as a powerful tool to dealing with complex nonlinear systems.Especially for the T-S fuzzy model,it can approximate a complex nonlinear system with arbitrary precision in the form of linear system weighted sum.Thus the analysis for the stability of T-S fuzzy system and controller design have received much attention.However,in actual industrial control,time-delay is one of the important factors leading to system instability.Therefore,the research on time-delay sys-tems has a wide range of practical applications.This paper mainly studies the design prob-lem of premise mismatch controller for time-delay systems with external disturbances;Stabilization problem for time-delay systems with parameter uncertainties;Robust H?performance analysis and controller design for time-delay systems with both parameter uncertainties and external disturbances.The main research results of this paper include the following three parts:First:A controller design problem based on interval type-2 T-S model nonlinear time-delay fuzzy systems is studied.According to the Lyapunov stability theory com-bined with the scaling inequalities of the matrix inequalities,the sufficient conditions for the closed-loop system to be asymptotically stable and satisfy the given H? performance index are derived.By using the characteristics of the type-two fuzzy basis functions that premise mismatch,a system stability criterion with less conservativeness is obtained.The simulation example partially verifies the effectiveness of the design method.Second:A delay-dependent robust stabilization problem for a class of T-S models with parametric uncertainties is studied.Constructing the Lyapunov-Krasovskii function-al,using the scaling technique of matrix inequality to solve the problem that the nonlinear term in the matrix cannot be solved,the sufficient conditions for the robust stabilization of the system are obtained.Combined with the characteristics of the two-type fuzzy basis function,a less conservative condition is obtained.Third:The design problem of a robust HOO controller based on interval type-2 T-S model with nonlinear time-delay systems with parameter uncertainties and external distur-bances is studied.Construct a new Lyapunov-Krasovskii functional,using the improved free weight matrix method,combined with Schur complement lemma,get the system asymptotically stable and satisfy the given H? Sufficient conditions for performance in-dicators.There is no scaling of any inequality in the entire proof process,so the resulting robust stability is less conservative.