Sampled-data H_∞ state-feedback control of systems with state delays

The finite horizon piecewise-constant state-feedback H^∞control of time-invariant linear systems with a finitenumber ofpoint and distributed time-delays is considered. For the controller, coupled Riccati type partial differential equationsbetween sampling and updating the terminal conditions are derived. For small time delays the solutions and the resultingcontrollers are approximated by series expansions in powers of the largest delay. Unlike the infinite horizon case, theseapproximations possess both regular and boundary layer terms. It is shown that the controller obtainedby high-orderapproximations improves the performance of thesystem. The performance of the closed-loop system under thememorylesszero-approximation controller is analysed. Bounded Real Lemmas for state-delay systems with jumps are obtained.