Homogeneous State Feedback Stabilization of Homogenous Systems

Titelangaben

Grüne, Lars:
Homogeneous State Feedback Stabilization of Homogenous Systems.
In: SIAM Journal on Control and Optimization. Bd. 38 (2000) Heft 4 . - S. 1288-1308.
ISSN 1095-7138
DOI: https://doi.org/10.1137/S0363012998349303

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Abstract

We show that for any asymptotically controllable homogeneous system in euclidian space (not necessarily Lipschitz at the origin) there exists a homogeneous control Lyapunov function and a homogeneous, possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system. If the system satisfies the usual local Lipschitz condition on the whole space we obtain semi-global stability of the sampled closed loop system for each sufficiently small fixed sampling rate, if the system satisfies a global Lipschitz condition we obtain global exponential stability for each sufficiently small fixed sampling rate. The control Lyapunov function and the feedback are based on the Lyapunov exponents of a suitable auxiliary system and admit a numerical approximation.