On the stable ℋ∞ controller parameterization under sufficient condition

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