Interactor extraction approach to matrix factorizations and singular optimal control

This paper proposes a method for various factorizations of strictly proper rational matrices, and then applies the method to singular optimal control problems, i.e., H₂ or H_∞ control where a standard assumption fails. By making full use of what is called “interactor extraction” of the rational matrices, this method reduces the problem to that of factorization of matrices having full rank at infinity. In contrast to the existing method that uses descriptor representation, the proposed method solely uses traditional state space methods, and hence is expected to be numerically more reliable