Stabilizability of bimodal piecewise linear systems with continuous vector field

Abstract

This chapter focuses on the 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 turns out that this system class inherits the relationship between controllability and stabilizability of linear systems. Controllability and stabilizability of a linear system are two basic concepts that were born in the early sixties. They have played a central role in various problems throughout the history of modern control theory. As such, these concepts have been studied extensively. © 2006 Elsevier Ltd All rights reserved.