Stabilization of switched linear systems with constrained inputs

The stabilization of switched linear systems with constrained inputs (SLSCI) is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time (MDT) to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system’s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.