Midpoint-Based Balanced Truncation for Switched Linear Systems With Known Switching Signal

We propose a novel model-reduction approach for switched linear systems with a 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.