Homogeneous control Lyapunov functions for homogeneous control systems

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Grüne, Lars:
Homogeneous control Lyapunov functions for homogeneous control systems.
In: el Jai, Abdelhaq (Hrsg.): Mathematical Theory of Networks and Systems. - Zielona Gora : Techn. Univ. Press , 2001

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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.