On the stable H-infinity controller parameterization under sufficient condition

Abstract

Suboptimal H(infinity) controller is said to internally stabilize the closed loop transfer matrix. However, the stability of controller is not assured in conventional H(infinity) control theory. Unstable controller can damage the whole system when the sensor fails or actuator saturates. This note presents a stable n-dimensional H(infinity) controller and its parameterization for the LTI system based on the sufficient condition for existence of stable H(infinity) controller. The stability of H(infinity) controller and closed-loop transfer matrix are guaranteed if the positive-semidefinite solutions for the suggested three Riccati equations exist.