Near-optimal interpolation-based time-limited model order reduction

Abstract

This paper presents an interpolatory framework for model order reduction of linear time-invariant (LTI) systems over limited time intervals of the form $[0,\tau ]$, with $\tau <\mathrm{\infty }$. We give a new proof for deriving interpolation-based first-order necessary conditions for time-limited $H_2$ optimality. Based on these optimality conditions, we propose a time-limited rational Krylov framework for time-limited rational interpolation. The interpolatory framework is used to present an iterative algorithm that yields reduced-order models satisfying the optimality conditions approximately. The distance to optimality is quantified in terms of the interpolation errors. The errors depend primarily on the interpolating model's poles and the time interval size. We test the proposed algorithm in three numerical examples and compare its performance with various time-limited model reduction algorithms available in the literature.

Keywords:

• Model order reduction
• linear time-invariant (LTI) systems
• rational Krylov methods
• time-limited $H_2$ optimality

Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed and constructive comments, which have contributed significantly to improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).