Stability of discrete-time conewise linear inclusions and switched linear systems

This paper addresses the stability of discrete-time conewise linear inclusions (CLIs) and its connection with that of switched linear systems (SLSs). The CLIs form a class of switched linear systems subject to state dependent switchings. Strong and weak stability concepts of the CLIs are considered and the equivalence of asymptotic and exponential stability is established. To characterize stability of the CLIs, a Lyapunov framework is developed and a converse Lyapunov theorem is obtained. Furthermore, stability of general SLSs is studied and is shown to be closely related to that of the CLIs through a family of properly defined generating functions.