Optimal model reduction of discrete-time descriptor systems

Abstract

An optimal model reduction method is presented to obtain stable reduced-order models for discrete-time descriptor systems. A parametrization based on the bilinear Routh approximation of linear normal discrete-time systems is used to parametrize the causal subsystems of the reduced-order models. The expressions for the error and its gradient are explicitly given. They are then employed to solve an unconstrained optimization problem for the model reduction problem. The descriptor system structure is preserved in the reduced-order models.