A Universal Formula for Stabilization with Bounded Controls

Authors: Yuandan Lin, Eduardo D. Sontag

Published: 1991 (Journal Paper)

Source: Systems & Control Letters

Algorithm: Sontag universal formula

DOI: 10.1016/0167-6911(91)90111-Q

Summary

Extends Sontag-style universal control-Lyapunov feedback to bounded controls, giving an explicit stabilizing formula under a known CLF. It sits next to Artstein theorem as a constructive bridge from CLF existence to feedback design.

Abstract

We provide a formula for stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin and continuous everywhere, is known to exist via Artstein's Theorem. As in the unbounded-control case treated in a previous note, we provide an explicit and 'universal' formula given by an algebraic function of Lie derivatives. In particular, we extended to the bounded case the result that the feedback can be chosen analytic if the Lyapunov function and the vector fields defining the system are analytic.

Links

Primary

Paper academia.edu

Standard

DOI 10.1016/0167-6911(91)90111-Q

Alternate

sciencedirect.com sciencedirect.com

Tags

• Control Lyapunov functions

• Stabilization

• Bounded controls

• Nonlinear control

• Artstein theorem

• Feedback control