Kybernetika 53 no. 5, 853-867, 2017

Stabilization of nonlinear systems with varying parameter by a control Lyapunov function

Wajdi Kallel and Thouraya KharratDOI: 10.14736/kyb-2017-5-0853

Abstract:

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.

Keywords:

Lyapunov function, feedback stabilization, nonlinear control systems, homogeneous system, finite time stability

Classification:

93D05, 93D15

paper.pdf

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