Model reduction of discrete linear systems via frequency-domain balanced structure

In this paper, a novel model reduction technique for discrete linear time invariant systems is presented. The proposed technique is based on a conceptual viewpoint of the controllability and the observability Grammian balancing of a discrete system in an arbitrary frequency range of operation. It could be viewed as the generalization of the Moore´s balance structure approach in a specific frequency range of operation. Two modified Lyapunov equations are derived for the proposed frequency-domain balancing. Various properties of the reduced model such as controllability, observability, stability, its uniqueness, and the error bound are examined. A comparison study of the proposed method with the Moore´s time domain technique is presented using a sixth-order digital filter