A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties

This paper investigates the problem of guaranteed cost control for Takagi-Sugeno fuzzy dynamic systems with interval parameter uncertainties. The parameter uncertainty is characterized by the matrix bound, which is quite natural in real applications. Attention is focused on the fuzzy state feedback controller design via the so-called parallel distributed compensation scheme, which guarantees the closed-loop system to be robustly stable with a prescribed upper bound of the cost function. By utilizing the instrumental idea of delay dividing, a new Lyapunov-Krasovskii functional is introduced, which leads the resultant conditions to be much less conservative than most existing results in the literature. Some other new ideas such as basis dependence are also employed, which help to reduce the conservatism. All the results are formulated in the form of linear matrix inequalities (LMIs), which can readily be solved via standard numerical software. Finally, illustrative examples are given to show the less conservatism and applicability of the obtained results.