Homogeneous state feedback stabilization of homogeneous systems

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Grüne, Lars:
Homogeneous state feedback stabilization of homogeneous systems.
Bayreuth , 2000

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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. We also show the relation between the degree of homogeneity and the bounds on the sampling rates which ensure asymptotic stability.