Exponential stability analysis and controller design of fuzzy systems with time-delay

Takagi–Sugeno (T–S) fuzzy models can provide an effective representation of complex nonlinear systems with a series of linear input/output submodels in terms of fuzzy sets and fuzzy reasoning. In this paper, the T–S fuzzy model approach is extended to the stability analysis and controller design for nonlinear systems with time delays. An improved stability condition is proposed by introducing adjustable parameters into the Lyapunov–Krasovskii functional. Stabilization approach for fuzzy state feedback is also presented. Sufficient conditions for the existence of fuzzy feedback gain are derived through the numerical solution of a set of obtained linear matrix inequalities (LMIs). Compared with the existing methods in the literature, the proposed approach has less conservatism and both the sizes of delay and its derivative are involved in the criterion. The dynamical performance of the system can be adjusted by changing the adjustable parameters. Finally, two examples are given to show the effectiveness of the proposed approach.