Reduced realization for switched linear systems with known mode sequence

Abstract

We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input–output behavior. A key feature of our method is that only the mode sequence of the switching signal needs to be known and not the exact switching times. Since simple examples show that a minimal realization will depend on the switching times, our algorithm cannot result in a minimal realization in general, but we conjecture that it results in a minimal realization for almost all switching times. Our approach is based on considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition.