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 view point of the controllability and observability Grammians balancing of a system in an arbitrary frequency range. It can be considered as the generalization of the Moore's balance structure approach [1] 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.