Model Reduction Using Parameterized Limited Frequency Interval Gramians for 1-D and 2-D Separable Denominator Discrete-Time Systems

In this paper, we propose model reduction algorithms based on the frequency-domain interval Gramians for 1-D and separable denominator 2-D discrete-time systems using balanced truncation as a parameterized combination of unweighted and the limited-frequency interval Gramians. The values of free parameters are computed using a line search optimization. The proposed algorithms provide a substantial improvement in the approximation error than the well-known existing techniques and generate stable reduced models along with an easily computable error-bound. The effectiveness of proposed algorithms is validated with the help of numerical examples of a sixth-order elliptic low-pass filter and a (6, 6)-order Roesser model of a separable denominator 2-D system.