Model Reduction for Systems with Inhomogeneous Initial Conditions
For control engineers and researchers, this provides a more flexible and accurate model reduction technique for systems with indeterminate initial conditions, though it is an incremental improvement over existing methods.
This paper addresses model reduction for linear systems with nonzero initial conditions by decomposing the response into unforced and forced components, reducing each independently, and combining them. The method offers better approximation properties than comparable approaches.
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.