On stable ℋ∞ controller parameterization using doubly coprime fractional representation

A suboptimal ℋ_∞ controller is said to internally stabilize the closed loop transfer matrix. However, the stability of controller is not assured in conventional ℋ_∞ control theory. An unstable controller can damage the whole system when the sensor fails or actuator saturates. The sufficient condition for the existence of stable ℋ_∞ controller is suggested. The paper presents the stable n-dimensional ℋ_∞ controller and its parameterization based on the suggested sufficient condition for the linear time invariant systems using doubly coprime factorization. The stability of the ℋ_∞ controller and closed-loop stability are guaranteed if the positive semi-definite solutions for the suggested three Riccati equations exist