Abstract
In this paper we establish the interpolatory model reduction framework for optimal approximation of MIMO dynamical systems with respect to the H2 norm over a finite-time horizon, denoted as the H2(tf) norm. Using the underlying inner product space, we derive the interpolatory first-order necessary optimality conditions for approximation in the H2(tf) 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.
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