Robust Decentralized Fuzzy Control for Large-scale Descriptor Systems With Decay Rate Constraint

Abstract

This study addresses the control problem of a nonlinear large-scale descriptor system (LSDS) through the use of a decentralized proportional-plus-derivative state feedback fuzzy (DPDF) control strategy. The Takagi-Sugeno (T-S) fuzzy modeling technique, which is widely used by researchers, is used to describe the nonlinear LSDS as a set of linear subsystems with interconnections. Based on the constructed T-S fuzzy LSDS, a DPDF feedback method is proposed to address the limitations of the descriptor matrix of the T-S fuzzy LSDS and to solve the regular and impulse-free problems of systems while providing a more convenient and effective approach for discussing system stability. Additionally, the Lyapunov theory is chosen to analyze the stability conditions. This study uses a quadratic Lyapunov function to provide sufficient criteria to ensure the decay rate performance of the LSDS, which can be transformed into linear matrix inequality (LMI) form. The proposed method is demonstrated through several examples to showcase its effectiveness.