Bimodal and Linear Switched Systems

Abstract

The chapter considers some special topics related to controllability and stabilizability of linear switching systems. While providing a short overview on the most important facts related to the topic it is shown how fundamental role is played by the finite switching property in obtaining the controllability and stabilizability results. The (closed–loop) stabilizability problem of controlled linear switched systems is also revisited. It is shown that the completely controllable sampled switching system can be robustly stabilized (against disturbances and model uncertainties) with suitable linear feedbacks and a periodic switching strategy. A self contained treatment of the bimodal LTI problems is also provided pointing to the relevant structures of the problem. It is shown that for a certain class of bimodal systems controllability in case of closed–loop switching systems is equivalent with controllability of an open–loop switching system using nonnegative controls, i.e., to the controllability of a constrained open–loop switching system.