On the stable 𝒽∞ controller parameterization under sufficient condition

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

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