Optimal model reduction of discrete-time systems

Abstract

Closed-form expressions of transfer function responses are used in this paper towards model-reduction of nth order discrete-time systems. The contribution of each eigenvalue to the output for a unit step input is evaluated, thus defining the dominant eigenvalues. The reduced-order model is set up retaining the most contributing eigenvalues, maintaining the same DC gain as the original system, but leaving other numerator coefficients to be determined. Then a cost function is formed measuring the discrete pulse response deviation between the original and the reduced-order model. The cost function is subsequently minimized, rendering new numerator coefficients for the reduced model. The resulting reduced-order model is easily computed, maintains stability for an originally stable system, and renders time responses practically identical to the original system.