Finite-time control of linear systems under time-varying sampling

In this work, the finite-time control problem for sampled-data systems is investigated. The time-varying sampling is not required to be periodic, and the only assumption is that the distance between any two consecutive sampling instants does not exceed a given bound. First, the continuous-time systems with digital control are modeled as continuous-time systems with delayed control input. Then, a novel Lyapunov functional is used to solve the finite-time control problem. At last, sufficient conditions for the existence of state feedback finite-time controller are obtained by solving a set of linear matrix inequalities (LMIs). Different from many existing finite-time control designs of linear systems, this work extends the partial results to the sampled-data systems. The effectiveness of the proposed results is eventually illustrated by a numerical example.