Optimal Fuzzy Tracking Synthesis for Nonlinear Discrete-Time Descriptor Systems with T-S Fuzzy Modeling Approach

Abstract

An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation (PDC) approach and the Proportional-Difference (P-D) feedback framework. Based on the Takagi-Sugeno Fuzzy Descriptor Model (T-SFDM), a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems, which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process. Leveraging the P-D feedback fuzzy controller, the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system. In view of the disturbance problems, a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy. To achieve a better balance between state and control responses, the H2 performance requirement is considered and a minimization constraint is applied to optimize the H2 index. It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems. Extending the Lyapunov theory, a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints. Finally, two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.