Sampled-data H-infinity state-feedback control of systems with state delays

The finite horizon piecewise-constant state-feedback H-infinity control of time-invariant linear systems with a finite number of point and distributed time-delays is considered. For the controller, coupled Riccati type partia l differential equations between sampling and updating the terminal conditi ons are derived. For small time delays the solutions and the resulting cont rollers are approximated by series expansions in powers of the largest dela y. Unlike the infinite horizon case, these approximations possess both regu lar and boundary layer terms. It is shown that the controller obtained by h igh-order approximations improves the performance of the system. The perfor mance of the closed-loop system under the memoryless zero-approximation con troller is analysed. Bounded Real Lemmas for state-delay systems with jumps are obtained.