New robust H∞ control approach for discrete T-S fuzzy time-delay system

A new piecewise Lyapunov-Krasovskii function approach on the stability analysis and the robust H∞ controller design of the discrete T-S fuzzy time-delay system is studied in this paper. Based on the definition of maximal overlapped-rules group, the systematic design of the fuzzy robust H∞ controller is investigated via parallel distributed compensation control scheme. And for the closed-loop discrete T-S fuzzy time-delay system, a new sufficient stability condition is proposed. This sufficient condition only requires finding common matrices in each maximal overlapped-rules group. The proposed condition is less conservative and difficult than the common Lyapunov-Krasovskii function approach and the fuzzy Lyapunov-Krasovskii function approach. Lastly, the simulation results show the effectiveness of the proposed approach.