A full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs

This paper studies open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case.