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On reachable set bounding for delayed discrete-time Takagi-Sugeno fuzzy systems

The purpose of this paper to study the reachable set bounding problem for discrete-time Takagi-Sugeno (T-F) fuzzy systems with time-varying delay under zero initial conditions. The key idea is to introduce the reciprocally convex combination approach for bounding the forward difference of triple-summable terms. Combining with some novel zero equalities, sufficient conditions are proposed to ensure that all the states of the system starting from origin are bounded in an ellipsoid. Simulation results are provided to demonstrate the validity of the theoretical findings.