J-Spectral Factorization and Generalized Algebraic Riccati Equation for Descriptor Systems with Infinite Zeros

Abstract

In this paper we consider a J-spectral factorization associated with a model matching problem for descriptor systems that contains non-proper systems as a special case. We do not assume that the plant has no invariant zeros at infinity. The existence of solutions to the model matching problem is shown to be equivalent to the J-spectral factorization. The J-spectral factor is constructed by a stabilizing solution of a generalized algebraic Riccati equation that is non-regular type. We also provide solvability conditions of the generalized Riccati equations and a computation method by considering a generalized eigenvalue problem. The results are natural extensions for a standard state space case.