Finite-time control of sampled-data systems

Finite-time control of sampled-data systems are addressed. A kind of Lyapunov-Krasovskii function-like function is proposed, whose derivative does not need to be negative definite. Based on input-delay approach and free-weight matrix technologies, sufficient conditions which can ensure finite-time stability (FTS) for the resulted closed-loop system with rapid time-vary delay are given in linear matrix inequalities (LMIs). And then in virtue of the results on finite-time stability, the state feedback controller is designed. These conditions are given in terms of LMIs and are delay-dependent.