A complete parameterization of clf-based input-to-state stabilizing control laws

• Published in: International journal of robust and nonlinear control Vol. 14; no. 17; pp. 1393 - 1420
• Main Authors: Curtis, J. W., Beard, Randal W.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 25.11.2004
• Subjects: input-to-state; iss; iss-clf; satisficing
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.961

Sontag's formula proves constructively that the existence of a control Lyapunov function implies asymptotic stabilizability. A similar result can be obtained for systems subject to unknown disturbances via input‐to‐state stabilizing control Lyapunov functions (ISS‐clfs) and the input‐to‐state analogue of Sontag's formula. The present paper provides a generalization of the ISS version of Sontag's formula by completely parameterizing all continuous ISS control laws that can be generated by a known ISS‐clf. When a simple inner‐product constraint is satisfied, this parameterization also conveniently describes a large family of ISS controls that solve the inverse‐optimal gain assignment problem, and it is proved that these controls possess Kalman‐type gain margins. Copyright © 2004 John Wiley & Sons, Ltd.