Receding horizon H∞ control for systems with a state-delay

This paper proposes the receding horizon H-infinity control (RHHC) for linear systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terms, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H-infinity-norm boundedness of the closed-loop system controlled by the proposed RHHC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon H-infinity-norm bound.