Controllability and stabilizability of discontinuous bimodal piecewise linear systems

Characterizing controllability like properties of bimodal piecewise linear systems, i.e., piecewise linear systems with two modes, is known to be a notoriously hard. In this chapter, we focus on discontinuous bimodal systems that are wellposed in the sense of existence and uniqueness of solutions. The main results of the chapter are Popov–Belevitch–Hautus-type necessary and sufficient conditions for controllability and stabilizability of such systems.