Fuzzy control with passivity synthesis for continuous affine Takagi‐Sugeno fuzzy systems

Abstract

Purpose The purpose of this paper is to propose a stability analysis and control synthesis for achieving passivity properties of a class of continuous‐time nonlinear systems. These nonlinear systems are represented via continuous affine Takagi‐Sugeno (T‐S) fuzzy models, which played an important role in nonlinear control systems. The affine T‐S fuzzy models are more approximate than homogeneous T‐S fuzzy models for modeling nonlinear systems. Using the energy concept of passivity theory with Lyapunov function, the conditions are derived to ensure the passivity and stability of nonlinear systems. Based on the parallel distribution compensation (PDC) technique, this paper proposes a fuzzy controller design approach to achieve the passivity and stability for the continuous affine T‐S fuzzy systems. Design/methodology/approach For solving stability and stabilization problems of affine T‐S fuzzy models, the conversion techniques and passive theory are employed to derive the stability conditions. By applying the linear matrix inequality technique, a modified iterative linear matrix inequality algorithm is proposed to determine and update the auxiliary variables for finding feasible solutions of these stability conditions. Findings By studying the numerical example, the proposed design technique of this paper is an effectiveness and useful approach to design the PDC‐based fuzzy controller. From the simulation results, the considered nonlinear system with external disturbances driven by proposed design fuzzy controller is stable and strictly input passive. Originality/value This paper is interesting for designing fuzzy controller to guarantee the stability and strict input passivity of affine T‐S fuzzy models.