Minimal realization for linear switched systems with a single switch

Abstract

We discuss the problem of minimal realization for linear switched systems with a given switching signal and present some preliminary results for the single switch case. The key idea is to extend the reachable subspace of the second mode to include nonzero initial values (resulting from the first mode) and also extend the observable subspace of the first mode by taking information from the second mode into account. We provide some simple examples to illustrate the approach.

Reduced realizations and model reduction for switched linear systems

“…The following parts of this thesis are already published or submitted for publication. Chapter 3 has been presented at the European Control Conference (ECC 2021) and published in [59]. A brief version of Chapter 4 will be presented at the 10th International Conference on Mathematical Modelling (MATHMOD 2022) in Vienna, Austria, and this chapter has also been submitted for journal publication.…”