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

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 (C) 2004 John Wiley Sons, Ltd.