Periodic stabilization of discrete-time controlled switched linear systems

The goal of this paper is to study the state-feedback stabilization of controlled discrete-time switched linear systems (SLSs), where the discrete switching control input and the continuous control input coexist. We propose a periodic hybrid-control policies, periodic control Lyapunov functions (PCLFs), and prove that the existence of a quadratic PCLF is a necessary and sufficient condition for the stabilizability of SLSs. Moreover, computational algorithms are developed to find quadratic PCLFs and test the stabilizability.