Stabilization Of Hybrid Systems Under State Constraints

This paper investigates the stabilization problem for a class of hybrid systems under state constraints. Emphasis is placed on the state constraints which are converted into the state saturation problem. Due to the existence of state saturation, the flow time consists of saturated and unsaturated time. Subsequently, sufficient conditions on uniformly globally pre-asymptotic stability (UGpAS) of hybrid systems are derived. As a valuable application, the results are extended to stabilize state-constrained switched systems under average dwell-time (ADT) switching by limiting the states in a unit hypercube. By resorting to the hybrid system description, an improved stabilization approach for switched systems with ADT is developed. The controller gains of the switched system can be designed by combining the method of convex hull vector and an iterative algorithm. Numerical simulation results for switched systems are provided to illustrate the feasibility of the proposed method. (C) 2021 Elsevier Ltd. All rights reserved.