A parametric optimization approach to discrete-time model reduction

Abstract

A new optimization method is presented to obtain stable reduced order models of a linear stable discrete-time system under l2 optimality. The number of delay operators may be imposed in advance in the reduced order models. The state-space bilinear Routh canonical realization is used to parametrize the reduced model and the optimal parameters are obtained by solving a gradient-based unconstrained optimization problem. Explicit gradient formulas are available for numerical implementation. The stability of the reduced models is ensured in the iteration process. The formulation can be easily modified to achieve zero steady-state response error for a unit step without affecting the unconstrained nature of the optimization. Numerical examples are used to illustrate the effectiveness of the proposed method.