A weighted balanced realization of 2-D discrete systems

An innovative weighted structurally balanced realization of two-dimensional (2-D) discrete systems is proposed. Two auxiliary transfer-function matrices called the weighted-input-to-state and the state-to-weighted-output transfer-function matrices are first introduced. Based on these matrices, the controllability and observability grammians of the weighted system are defined and the existence of the grammians is justified. The resulting 2-D weighted structurally balanced realization method can be applied for the reduction of the system order of 2-D discrete systems.