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 , with . We give a new proof for deriving interpolation-based first-order necessary conditions for time-limited 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.