Abstract
The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov functions (CLF’s) defined by means of generalized derivatives. In this manner, one obtains a complete characterization of asymptotic controllability, applying in principle to a far wider class of systems than Artstein’s Theorem (which relates closed-loop feedback stabilization to the existence of smooth CLF’s). The proof relies on viability theory and optimal control techniques.
Supported in part by US Air Force Grant F49620-95-1-0101
Supported in part by NSF Grant DMS92-02554
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© 1996 Birkhäuser Verlag Basel
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Sontag, E.D., Sussmann, H.J. (1996). General Classes of Control-Lyapunov Functions. In: Jeltsch, R., Mansour, M. (eds) Stability Theory. ISNM International Series of Numerical Mathematics, vol 121. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9208-7_10
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DOI: https://doi.org/10.1007/978-3-0348-9208-7_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9945-1
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