AN ALGEBRAIC RICCATI EQUATION APPROACH TO H-INFINITY OPTIMIZATION

This paper considers the general (so-called four block) H** infinity optimal control problem with the assumption that system states are available for feedback. It is shown that optimization of the H** infinity norm of the closed loop transfer function over all linear constant, i. e. , nondynamic, stabilizing state feedback laws can be completely characterized via an algebraic Riccati equation. It is further shown that the optimal norm is not improved by allowing feedback to be dynamic. Thus, the general state-feedback H** infinity optimal control problem can be solved by iteratively solving one ARE and the controller can be chosen to be static gain.