Controllability and stabilizability of linear switched systems

The paper consider some special topics related to controllability of linear switching systems. Consequences of the normal controllability property and controllability under sampling are investigated. Both problems are related to the existence of a finite switching sequence with certain properties. It is shown that completely controllable linear switching systems, regardless to the sign of the allowed controls, contains a completely controllable linear time-varying system. 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.