Stabilization analysis for discrete-time fuzzy systems via nonuniform delay partitioning technique

This paper is concerned with the stability analysis problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By utilizing the idea of partitioning the delay interval into l nonuniform subintervals and the reciprocally convex technique, a novel fuzzy Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. The conservatism reduction becomes more obvious with the partitioning getting thinner. Then, on the basis of parallel distributed compensation (PDC) law, the state-feedback fuzzy controller can be obtained for the concerned fuzzy delayed systems. These proposed conditions are given in terms of linear matrix inequalities, which can be solved by standard numerical software.