On controllability and stabilizability of some bimodal LTI systems

This paper investigates controllability of a class of bimodal linear time invariant (LTI) systems pointing to the relevant structures of the problem. It is shown that for a certain class controllability 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. The paper gives some algebraic conditions that guarantees global controllability for this class of systems. It is shown that if the system is globally controllable then the number of necessary switchings to control the system is bounded. It is also shown that global controllability implies stabilizability for this class of systems.