H∞-optimal one-step-ahead output feedback control of discrete-time systems

The discrete-time, one-step-ahead, standard four-blocks H_∞-optimal control problem is considered. The output feedback problem is transformed into a one-step-ahead H_∞-optimal state-estimation problem and the existing solution is used to derive the controller. It is assumed that only previous measurements are available for control. Two results are obtained. The first requires the solutions of two coupled Riccati equations, where the necessary and sufficient condition for the existence of the H_∞-optimal result requires only the positive semidefiniteness of these solutions. The second result applies two decoupled Riccati equations with a coupling constraint, as in the continuous-time case, and two additional conditions. The derivation procedure is most simple and may thus provide considerable insight into the solution of the discrete-time standard problem. A similar procedure can also be used to obtain a solution to problems where the current measurement is available