An Optimal Divisioning Technique to Stabilization Synthesis of T–S Fuzzy Delayed Systems

This paper investigates the problem of stability analysis and stabilization for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov–Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T–S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.