A universal formula for asymptotic stabilization with bounded controls

• Main Authors: Yuandan Lin, Yuandan Lin, Sontag, Eduardo D.
• Format: Article
• Published: Institute of Advanced Engineering and Science 2015
• Subjects: TK Electrical engineering. Electronics Nuclear engineering
• Online Access: http://eprints.utm.my/id/eprint/57683/; http://eprints.utm.my/cgi/users/home?screen=EPrint%3A%3AEdit&eprintid=57683&stage=core

We provide a formula for a stabilizing feedback law using a bounded control, under theassumption that an appropriate control-Lyapunov function is known. Such a feedback,smooth awayfrom the origin and continuous everywhere, is known to exist via Artstein'sTheorem. As in the unbounded-control case treated in a previous note, we provide anexplicit and \universal" formula given by an algebraic function of Lie derivatives. Inparticular, we extend to the bounded case the result that the feedback can be chosenanalytic if the Lyapunov function and the vector elds de ning the system are analytic.