Homogeneous state feedback stabilization of homogeneous systems

L. Grüne: Homogeneous state feedback stabilization of homogeneous systems
SIAM Journal on Control and Optimization 38, 1288 - 1214, 2000

DOI: 10.1137/S0363012998349303
Keywords: homogeneous feedback; control Lyapunov function; Lyapunov exponents; stabilization; discretized feedback
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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.

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