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 partial differential equations between sampling and updating the terminal conditions are derived. For small time delays the solutions and the resulting controllers are approximated by series expansions in powers of the largest delay. Unlike the infinite horizon case, these approximations possess both regular and boundary layer terms. It is shown that the controller obtained by high-order approximations improves the performance of the system. The performance of the closed-loop system under the memoryless zero-approximation controller is analysed. Bounded Real Lemmas for state-delay systems with jumps are obtained.