Extended Dissipativity Controller Design For Interval Type-2 T-S Fuzzy Systems

The proposed interval type-2 fuzzy systems brings novel research ideas and methods for further study on uncertain nonlinear systems,which make it possible to analyze stability,design controller and filter for interval type-2 Tagaki-Sugeno?T-S?fuzzy systems by utilizing the results of type-1 T-S fuzzy systems.Moreover,as a extension of dissipativity,extended dissipativity is a very important performance for nonlinear systems,which covers the H_? performance,the L₂-L_? performance and the passivity that often appears in letters.For interval type-2 discrete time T-S fuzzy systems,the problems of generalized H₂ controller design,extended dissipativity analysis and state feedback controller design are investigated in this thesis.The main results are divided into the following three parts.Part ?: The generalized H₂ controller design problem is investigated for a class of interval type-2 discrete-time fuzzy systems with uncertainties.Using matrix inequality techniques and Lyapunov approach,a sufficient condition for asymptotic stability of the close-loop systems with generalized H₂-norm bound is developed.Relaxed matrixes are introduced with the properties of type-2 fuzzy basis functions,matrix decomposition techniques are adopt to deal with parameter uncertainties.Finally,the simulation results demonstrate the feasibility of the derived method.Part ?: According to the definition of extended dissipativity in discrete-time T-S fuzzy systems,by using basis-dependent Lyapunov functions and introducing an extra matrix to decouple the Lyapunov function matrix,sufficient conditions of the extended dissipativity are derived.Then,the problems of extended dissipativity analysis for discrete-time T-S fuzzy systems with time-varing delay are investigated.By using free-weighting matrixes method and introducing a triple-summable term in Lyapunovkrasovskii functional,the reciprocally convex approach is utilized to bound the forward difference and then the extended dissipativity criterion for the underlying systems is derived.Part ?: The problems of extended dissipativity analysis and state feedback controller design are investigated for a class of interval type-2 discrete-time T-S model nonlinear systems with time-varying delays.By employing model transformation method,the system underlying can be decomposed into a linear time-invariant subsystem and a norm-bounded uncertain subsystem.A sufficient asymptotic stability condition of the extended dissipativity is established by a delay-dependent Lyapunov-Krasovskii functional.Next,the requirements of the two related matrices of Lyapunov-Krasovskii functional are relaxed from positive definite to symmetry.And the positive definite constraints of Lyapunov-Krasovskii functional are introduced,then a new stability and extended dissipativity condition is derived.Finally,the simulation demonstrates the effectiveness of the proposed extended dissipativity control method.