Optimal model reduction of discrete-time descriptor systems

An optimal model reduction method is presented to obtain stable reduced-ord er 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 t hen employed to solve an unconstrained optimization problem for the model r eduction problem. The descriptor system structure is preserved in the reduc ed-order models.