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Homogeneous State Feedback Stabilization of Homogeneous Systems (2000)
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BibTeX
@MISC{Grüne00homogeneousstate,
author = {Lars Grüne},
title = {Homogeneous State Feedback Stabilization of Homogeneous Systems},
year = {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 feedbacklaw 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. 1Introduction In this paper we consider the problem of asymptotic state feedback stabilization of homogeneous control systems in R n . This problem has been considered by anumber of authors during the last years, see e.g. [14, 15, 16, 17, 20, 21, 22, 24], to mention just a few examples. Homogeneous systems appear naturally as local approximations to nonlinear systems, cf. e.g. [13]. In order to make use of this approximation property in the design of locally stabilizing feedbacks for nonlinear systems the main idea lies in the construction of homogeneous ...
Keyphrases
homogeneous system homogeneous state feedback stabilization nonlinear system homogeneous control lyapunov function asymptotic state feedback stabilization homogeneous control system controllable homogeneous system asymptotic stability sampling rate main idea local approximation euclidian space last year discontinuous state feedbacklaw approximation property loop system
