Stability analysis and decentralized H∞ control for time-delay fuzzy interconnected systems via fuzzy Lyapunov-Krasovskii functional

Abstract

This paper is concerned with the stability analysis and H∞ fuzzy controller design of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of N interconnected time-delay Takagi-SugenoT-S fuzzy subsystems and the delay-dependent stability analysis is based on the fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is shown that the delay-dependent stability of the time-delay fuzzy interconnected systems can be established if a fuzzy weighting-dependent Lyapunov-Krasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities LMIs that are numerically feasible. The decentralized H∞ controllers are also designed by solving a set of LMIs based on these fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is demonstrated via numerical examples that the stability and controller synthesis results based on fuzzy weighting-dependent Lyapunov-Krasovskii functionals are less conservative than those based on the common quadratic Lyapunov-Krasovskii functionals.