Midpoint based balanced truncation for switched linear systems with known switching signal

We propose a novel model reduction approachfor switched linear systems with known switching signal. Theclass of considered systems encompasses switched systems withmode-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 theseGramians satisfy precise interpretations in terms of input andoutput energy. Based on balancing the midpoint Gramians, wepropose a piecewise-constant projection based model reductionresulting in a switched linear system of smaller size