Geodesic
Stabilization of nonlinear systems with varying parameter by a control Lyapunov function
Kybernetika, Tome 53 (2017) no. 5, pp. 853-867.

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In this paper, we provide an explicit homogeneous feedback control with the requirement that a control Lyapunov function exists for affine in control systems with bounded parameter that satisfies an homogeneous condition. We use a modified version of the Sontag's formula to achieve our main goal. Moreover, we prove that the existence of an homogeneous control Lyapunov function for an homogeneous system leads to an homogeneous closed-loop system which is asymptotically stable by an homogeneous feedback control. In addition, we study the finite time stability for affine in control systems with varying parameter.
DOI : 10.14736/kyb-2017-5-0853
Classification : 93D05, 93D15
Keywords: feedback stabilization; homogeneous system; nonlinear control systems; Lyapunov function; finite time stability 
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     title = {Stabilization of nonlinear systems with varying parameter by a control {Lyapunov} function},
     journal = {Kybernetika},
     pages = {853--867},
     publisher = {mathdoc},
     volume = {53},
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     year = {2017},
     doi = {10.14736/kyb-2017-5-0853},
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     zbl = {06861628},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0853/}
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Kallel, Wajdi; Kharrat, Thouraya. Stabilization of nonlinear systems with varying parameter by a control Lyapunov function. Kybernetika, Tome 53 (2017) no. 5, pp. 853-867. doi : 10.14736/kyb-2017-5-0853. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0853/

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