A weak Kalman decomposition approach for reduced realizations of switched linear systems

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

“…None of above model-reduction approaches for switched systems consider the switched system as a piece-wise constant linear timevarying system, i.e., the question how to reduce a switched system for a given (and known) switching signal. We have recently studied the question of reduced realization of switched systems [16], [17] and observed that the specific mode sequence as well as the mode durations influence the size of the minimal realization. Hence, it is reasonable to conclude that in the case of a known switching signal, the size of a reduced system that approximates the original input-output behavior sufficiently well will also depend on the particular switching signals.…”