Basis-dependent Lyapunov Function Approach To Control Design Of Nonlinear Systems Based On T-S Fuzzy Model

This paper mainly focuses on the control problem of T-S model based nonlinear systems using the basis-dependent Lyapunov function approach.Two kinds of such systems are considered,2-D T-S model based and interval type-2 T-S model based nonlinear systems.Firstly,the controllers of2-D nonlinear systems are developed via basis-dependent Lyapunov function.For 2-D T-S model based nonlinear systems,due to the vectors of the system change along two different directions,the effective results are obtained by the basis-dependent Lyapunov function which can be assigned to the two directions.Moreover,the basis-dependent function approach is extended to the interval type-2 fuzzy systems.Based on the cone complement algorithm,the generalized dissipative control problem for interval type-2 T-S model based nonlinear systems can be solved by combining the basisdependent function approach and the line integral-type Lyapunov function method.The main results can be divided into the following three parts:In the first part,it is concerned with the problem of the H?controller design for a class of 2-D T-S model based nonlinear systems.By employing basis-dependent Lyapunov function method,the 2-D nonlinear systems with linear fractional uncertainty is investigated,and less conservative sufficient conditions of prescribed noise attenuation are obtained.The controller with prescribed noise attenuation for 2-D nonlinear systems can be designed by the decoupling matrix method and the matrix decomposition technique.In the second part,the H?output feedback controller is designed for a class of uncertain 2-D T-S model based nonlinear systems.The sufficient conditions of the H?output feedback controller design are obtained via the basis-dependent Lyapunov function approach.Based on the sufficient conditions,the H?output feedback controller problem of 2-D T-S model based nonlinear systems with linear fractional uncertainty can be solved by the matrix decomposition method and Schur lemma.In the third part,we study the problem of the generalized dissipative controller design for a class of interval type-2 T-S model based nonlinear systems.A sufficient condition of asymptotical stability and generalized dissipativity for the closed-loop interval type-2 fuzzy logic system is proposed based on the line integral-type Lyapunov function method and the basis-dependent Lyapunov function approach.Since the existing decoupling matrix approaches are not suitable for generalized dissipative controller design directly,a new method of decoupling matrix is proposed to deal with the nonlinear problem.This kind of controller problem can be transformed into a minimum optimization problem with linear inequality constraints,which can be solved via cone complementarity linearization algorithm.Finally,a numerical example is given to show the effectiveness of the proposed results.