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Displaying similar documents to “Only a level set of a control Lyapunov function for homogeneous systems”

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...

Separation principle for nonlinear systems using a bilinear approximation

Mohamed Ali Hammami, Hamadi Jerbi (2001)

Kybernetika

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In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.

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...