Model reduction for linear systems with low-rank switching
For engineers working with large-scale switched systems, this provides a novel reduction approach that leverages low-rank structure, though the method is domain-specific.
The paper introduces a model order reduction method for linear switched systems with low-rank switching, using an envelope system to enable standard reduction techniques. Numerical examples demonstrate the method's efficacy.
We introduce a novel model order reduction method for large-scale linear switched systems (LSS) where the coefficient matrices are affected by a low-rank switching. The key idea is to replace the LSS by a non-switched system with extended input and output vectors - called the envelope system - which is able to reproduce the dynamical behavior of the original LSS by applying a certain feedback law. The envelope system can be reduced using standard model order reduction schemes and then transformed back to an LSS. Furthermore, we present an upper bound for the output error of the reduced-order LSS and show how to preserve quadratic Lyapunov stability. The approach is tested by means of various numerical examples demonstrating the efficacy of the presented method.