Constrained doubly coprime factorization for all stabilizing ℋ∞ controllers

The conventional Youla parameterization (equivalently Q-Parameterization) approach to solve ℋ∞ optimal control problems requires solving the well-known matrix dilation optimization as a method for satisfying the ℋ∞-norm constraint of the closed-loop transfer matrix. As an alternative, this paper presents a constrained doubly coprime factorization so that the ℋ∞-norm constraint of the closed-loop transfer matrix can be satisfied without the need for matrix dilation optimization. For a given ℋ∞-norm constraint, a constrained plant is suggested from a state estimator that includes the worst-case disturbance and estimation effects. Then, the constrained doubly coprime factorization is derived from the constrained plant model. All the stabilizing ℋ∞ controllers are expressed by using the constrained coprime factors. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.