Homogeneous control Lyapunov functions for homogeneous control systems

L. Grüne, F. Camilli, F. Wirth: Homogeneous control Lyapunov functions for homogeneous control systems
in: Proceedings of the Mathematical Theory of Networks and Systems (MTNS2000), CD-Rom, Article B99, Perpignan, 2000,

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Abstract:

We show that any asymptotically controllable homogeneous control system admits a homogeneous control Lyapunov function. As a consequence, we obtain that any such system admits a stabilizing discontinuous sampled feedback, where the sampling rate is bounded from below depending on the degree of the homogeneity. Furthermore, we show that asymptotic controllability of a homogeneous system implies local asymptotic controllability of an approximated system.

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