A Universal Formula for Stabilization with Bounded Controls

Authors

Yuandan Lin, Eduardo D. Sontag

Year

1991

Journal Paper

Algorithm

Sontag universal formula

Source

Systems & Control Letters

Identifiers

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

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.

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.