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

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.