has been accepted for publication in IEEE TAC and is already available as early access.
Hossain, Sumon; Trenn, Stephan
In: IEEE Transactions on Automatic Control, vol. 69, no. 1, 2024, (2023 early access).
We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size.