Stability analysis and H∞ controller design of fuzzy large-scale systems based on piecewise Lyapunov functions

Authors:
Hongbin Zhang;Chunguang Li;Xiaofeng Liao
Affiliations:
Center for Nonlinear & Complex Syst., Univ. of Electron. Sci. & Technol. of China, Chengdu, China;-;-
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
2005

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Abstract

This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise Lyapunov function can be constructed, and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H∞ controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.