Stabilization of a class of switched systems with state constraints

Abstract

This paper investigates the stabilization problem for a class of switched systems with state constraints in both continuous-time and discrete-time contexts. The state constraints are converted into state saturations by limiting the state in a unit hypercube. An improved average dwell time method is presented to take into account different decay rates of a Lyapunov function related to an active subsystem according to the saturations occurring or not. Sufficient conditions for stability and stabilizability of the switched system with state constraints are derived; meanwhile, the stabilizing state feedback controllers are designed. An application to a longitudinal motion of highly maneuverable aircraft technology (HiMAT) vehicle is given to illustrate the applicability and the effectiveness of the proposed method.