Reachable Set Estimation of T–S Fuzzy Systems With Time-Varying Delay

In this paper, the reachable set estimation problem is investigated for delayed discrete-time Takagi-Sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions. A reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple-summable terms. The derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set, and all the states from other domain converge exponentially within another compact set. Moreover, a less conservative stability condition is also obtained. The effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples.