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Keywords:
feedback stabilization; homogeneous system; nonlinear control systems; Lyapunov function; finite time stability
feedback stabilization; homogeneous system; nonlinear control systems; Lyapunov function; finite time stability
Summary:
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.
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