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Time-limited Gramians Based Model Reduction Framework for 1-D and 2-D Systems

Muhammad Imran*, Syeda Fizza Hamdani, and Muhammad Imran
International Journal of Control, Automation, and Systems, vol. 20, no. 11, pp.3540-3548, 2022

Abstract : Gawronski and Juang provide an unstable reduced-order model formulation without a priori error bounds for the original one- and two-dimensional models. Several strategies were put forth for the standard linear discretetime one-dimensional models to guarantee the stability of the reduced-order model over a given time-intervals. These frameworks produce significant truncation mistakes and lack time-domain error-bound expressions. For discrete-time, two-dimensional Gramians models, there are no stability-preserving frameworks that the authors are aware of. This study suggests a Gramian-based model reduction strategy for discrete-time models. One- and two-dimensional discrete-time models can be employed with the framework. The suggested model reduction approach is applied using time-limited Gramians after the discrete-time two-dimensional causal recursive separable denominator models are split into two sub-models (two one-dimensional cascaded models). The framework ensures reduced-order model stability and offers time-domain a priori error-bound expressions for one- and twodimensional models. Comparisons and numerical results demonstrate the usefulness of the proposed framework.

Keyword : "Minimal realization, minimal-rank decomposition, model reduction, time-limited Gramians. "

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