Stabilization of Large-Scale Fuzzy Interconnected System

Stabilization of Large-Scale Fuzzy Interconnected System

DOI: 10.4018/978-1-5225-2385-7.ch003

Abstract

The chapter addresses the stabilization problem for large-scale fuzzy interconnected systems. Our aim is to present the design results on both the state feedback and static-output feedback (SOF) stabilizing fuzzy controllers. Firstly, by using some bounding techniques, the reduced number of LMIs to the decentralized state feedback controller design will be derived. Then, by using some matrix transformation techniques and singular system approach, we will also derive some design results on decentralized SOF control in terms of LMIs. Moreover, the proposed design results on the decentralized control will be extended to address the distributed control problem. Finally, several examples are given to illustrate the use of corresponding results.
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3.2 Decentralized Stabilization Design

In this section, we will study decentralized stabilization for large-scale T-S fuzzy interconnected systems.

3.2.1 Problem Formulation

Consider a continuous-time large-scale nonlinear interconnected system containing subsystems with interconnections, where the -th nonlinear subsystem is represented by the following T-S fuzzy model:

Plant Rule : IF

THEN
(1) where , , is the number of the subsystems; is the fuzzy inference rule; is the number of inference rules; are fuzzy sets; and denotes the system state and control input, respectively; are the measurable variables; is the -th local model; denotes the nonlinear interconnection of the -th and -th subsystems.

Define the inferred fuzzy set and normalized membership function , it yields

(2) where we will denote for brevity, and is the grade of membership of in .

By fuzzy blending, the -th global T-S fuzzy dynamic model is obtained by

(3) where

(4)

A decentralized fuzzy controller is given by:

Plant Rule : IF is and is and and is , THEN

(5) where is controller gains to be determined.

Similarly, the overall controller can be given by

(6) where

Combined with the fuzzy system in (3) and the fuzzy controller in (6), the closed-loop fuzzy control system can be given by

(7)

In this section, our aim is to design a decentralized fuzzy controller (6), such that the closed-loop fuzzy control system is asymptotically stable.

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