Passive Decentralized Fuzzy Control for Takagi-Sugeno Fuzzy Model Based Large-Scale Descriptor Systems

This paper presents a decentralized control problem for stabilizing the nonlinear large-scale descriptor (LSD) systems that use the proportional-plus-derivative state (PD) feedback scheme. The descriptor systems have a great focus on the research because they can contain more physical characteristics than standard state-space systems. At first, each nonlinear subsystem in the LSD system can be represented by Takagi-Sugeno (T-S) LSD systems with interconnections. In order to be more realistic, we additionally consider external disturbances and perturbations that affect the system. Our goal is to design a decentralized (DPD) fuzzy controller, such that the T-S LSD system is stable while the external disturbances and perturbations that affect the system. For the controller design process, sufficient conditions were developed based on the quadratic Lyapunov approach, PD feedback scheme, robust constraint, passivity constraint, and linear matrix inequality (LMI) sufficient criteria. At last, two numerical examples are given to show the application of the main results.