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Preprint 15-2016

Model Reduction for Systems with Inhomogeneous Initial Conditions

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Author(s) : Christopher A. Beattie , Serkan Gugercin , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 15-2016

MSC 2000

34H05 Control problems
65L70 Error bounds

Abstract :
We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a superposition of the response map for an unforced system having nontrivial initial conditions and the response map for a forced system having null initial conditions, we develop a new approach that involves reducing these component responses independently and then combining the reduced responses into an aggregate reduced system response. This approach allows greater flexibility and offers better approximation properties than other comparable methods.

Keywords : Model reduction, inhomogeneous initial condition, balanced truncation, transfer map splitting, approximation error balancing, iterative rational Krylov algorithm

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