A new consideration for discrete-system reduction via impulse response Gramian

Abstract

Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix A, of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices b(r) and c(r) are obtained so that various initial Markov parameters and time-moments of the original system are preserved in the reduced model. In this paper a different approach is presented based on the recursive relationship among the impulse response Gramians.