Further Constructions of Control-Lyapunov Functions and Stabilizing Feedbacks for Systems Satisfying the Jurdjevic-Quinn Conditions

Details Further Constructions of Control-Lyapunov Functions and Stabilizing Feedbacks for Systems Satisfying the Jurdjevic-Quinn Conditions Further Constructions of Control-Lyapunov Functions and Stabilizing Feedbacks for Systems Satisfying the Jurdjevic-Quinn Conditions

2005-10-18

arxiv.org/abs/math/0510379v1

IEEE Transactions on Automatic Control, Volume 51, Number 2, pp. 360-365, February 2006

Mathematics

Optimization and Control

15 pages, 0 figures, accepted for publication in IEEE Transactions on Automatic Control in October 2005

Scientific paper

10.1109/TAC.2005.863500

For a broad class of nonlinear systems, we construct smooth control-Lyapunov functions whose derivatives along the trajectories of the systems can be made negative definite by smooth control laws that are arbitrarily small in norm. We assume our systems satisfy appropriate generalizations of the Jurdjevic-Quinn conditions. We also design state feedbacks of arbitrarily small norm that render our systems integral-input-to-state stable to actuator errors.

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