Delayed Impulsive Control of Takagi–Sugeno Fuzzy Delay Systems

In this paper, the problem of exponential stability for Takagi–Sugeno (T–S) fuzzy delay systems with delayed impulses is addressed. By means of the time-dependent Lyapunov function method combined with Razumikhin technique, a sufficient condition expressed in terms of linear matrix inequalities (LMIs) is obtained for exponential stability of T–S fuzzy delay systems with delayed impulses. The derived stability condition depends both on the lower bound and the upper bound of impulsive intervals, which is robust with respect to small impulse input delays. By solving a set of LMIs, an impulsive state feedback controller can be easily constructed. Two numerical examples are discussed to illustrate the effectiveness of the theoretical findings.