Development of Frequency Weighted Model Order Reduction Techniques for Discrete-Time One-Dimensional and Two-Dimensional Linear Systems With Error Bounds

Frequency weighted model reduction framework pretested by Enns yields an unstable reduced order model. Researchers demonstrated several stability preserving techniques to address this main shortcoming, ensuring the stability of one-dimensional and two-dimensional reduced-order systems; nevertheless, these approaches produce significant truncation errors. In this article, Gramians-based frequency weighted model order reduction frameworks have been presented for the discrete-time one-dimensional and two-dimensional systems. Proposed approaches overcome Enns’ main shortcoming in reduced-order model instability. In comparison to the various stability-preserving approaches, proposed frameworks provide an easily measurable
a priori
error-bound expression. The simulation results show that proposed frameworks perform well in comparison to other existing stability-preserving strategies, demonstrating the efficacy of proposed frameworks.