Lyapunov and feedback characterizations of state constrained controllability and stabilization

A standard control system is considered, in conjunction with a state constraint S and a target set Sigma. The properties of open loop S-constrained control to Sigma and practical closed loop S-constrained control to Sigma are shown to be equivalent, and to be characterizable in terms of the existence of certain types of control Lyapunov functions. Feedback S-constrained stabilizability to Sigma can be added to the list of equivalences, when a small time controllability property is posited. (C) 2004 Elsevier B.V All rights reserved.