Decentralized Multi-Performance Fuzzy Control for Nonlinear Large-Scale Descriptor Systems

Abstract

This article addresses the decentralized multi-performance (MP) fuzzy control problem of nonlinear large-scale descriptor (LSD) systems. The considered LSD system contains several subsystems with nonlinear interconnection and external disturbances, and the Takagi-Sugeno fuzzy model (TSFM) is adopted to represent each nonlinear subsystem. Based on the proportional-plus-derivative state feedback (PDSF) scheme, we aim to design a decentralized MP fuzzy controller that guarantees the stabilization, mixed H-infinity, and passivity performance control (MHPPC), and the guaranteed cost control (GCC) performance of the closed-loop Takagi-Sugeno LSD (TSLSD) systems. Furthermore, we introduce the Lyapunov stability theory and the free-weighting matrix scheme to analyze the stability of the TSLSD system. The proposed sufficient conditions can be transformed as linear matrix inequality (LMI) forms through Schur's complement, which can be easily solved with the LMI Toolbox. Finally, to illustrate the proposed approach, two examples and simulation results are presented.