${\mathcal{H}}_2(t_f)$ Optimality Conditions for a Finite-time Horizon

Abstract

In this paper we establish the interpolatory model reduction framework for optimal approximation of MIMO dynamical systems with respect to the ${\mathcal{H}}_2$ norm over a finite-time horizon, denoted as the ${\mathcal{H}}_2(t_f)$ norm. Using the underlying inner product space, we derive the interpolatory first-order necessary optimality conditions for approximation in the ${\mathcal{H}}_2(t_f)$ norm. Then, we develop an algorithm, which yields a locally optimal reduced model that satisfies the established interpolation-based optimality conditions. We test the algorithm on various numerical examples to illustrate its performance.

11 pages, 4 figures, 2 .tex file, 1 .bbl file

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