Displaying similar documents to “On the stabilizability of homogeneous systems of odd degree”

Only a level set of a control Lyapunov function for homogeneous systems

Hamadi Jerbi, Thouraya Kharrat (2005)

Kybernetika

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In this paper, we generalize Artstein’s theorem and we derive sufficient conditions for stabilization of single-input homogeneous systems by means of an homogeneous feedback law and we treat an application for a bilinear system.

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

Wajdi Kallel, Thouraya Kharrat (2017)

Kybernetika

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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...

Smooth homogeneous asymptotically stabilizing feedback controls

H. Hermes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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If a smooth nonlinear affine control system has a controllable linear approximation, a standard technique for constructing a smooth (linear) asymptotically stabilizing feedbackcontrol is via the LQR (linear, quadratic, regulator) method. The nonlinear system may not have a controllable linear approximation, but instead may be shown to be small (or large) time locally controllable via a high order, homogeneous approximation. In this case one can attempt to construct an asymptotically...