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

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-Sugeno(T-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. © 2014 - IOS Press.