Frequency-weighted balanced Truncation of 2-D separable denominator discrete-time systems

A frequency-weighted balanced truncation technique for two-dimensional (2-D) separable denominator discrete-time systems is presented that is applicable with single-sided and double-sided weights. The proposed method is straightforward and efficient than the existing methods as the computation of controllability and observability Gramians doesn’t require solutions of Lyapunov inequalities and iterative algorithms. The simulation results of numerical examples are given to demonstrate the effectiveness of the proposed approach.