Development of time-limited model reduction technique for one-dimensional and two-dimensional systems with error bound via balanced structure

Abstract

In this article, the two-dimensional model is decomposed into two one-dimensional models using the minimal rank-decomposition condition, and the model reduction is conducted on these two one-dimensional models using time-limited Gramians. The proposed framework works for both one-dimensional and two-dimensional systems. The suggested approach addresses the primary flaw in Gawronski & Juang’s problem of reduced-order model instability. Researchers revealed some stability preservation solutions to address this key flaw, which ensure the stability of one-dimensional reduced-order systems; nevertheless, these strategies result in large approximation errors. However, to the best of the authors’ knowledge, there is no literature available for the stability preserving time-limited-intervals Gramians based model reduction framework for the two-dimensional discrete-time systems. In comparison to other stability-preserving strategies, the proposed framework provides an a priori error-bound formulation that is easily computable. The simulation results show that the proposed framework performs well compared to other existing stability-preserving methods, demonstrating its usefulness.