Stabilization of homogeneous polynomial systems in the plane

Hamadi Jerbi; Thouraya Kharrat; Khaled Sioud

Displaying similar documents to “Stabilization of homogeneous polynomial systems in the plane”

On The Stabilizability of Homogeneous Systems Of Odd Degree

Hamadi Jerbi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.

Some dimensional results for a class of special homogeneous Moran sets

Xiaomei Hu (2016)

Czechoslovak Mathematical Journal

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We construct a class of special homogeneous Moran sets, called ${m_{k}}$ -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of ${m_{k}}_{k \geq 1}$ , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.

On the stabilizability of homogeneous systems of odd degree

Hamadi Jerbi (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.

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.

Positively homogeneous functions and the Łojasiewicz gradient inequality

Alain Haraux (2005)

Annales Polonici Mathematici

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It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on $ℝ^{N}$ satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.

Improving the performance of semiglobal output controllers for nonlinear systems

Abdallah Benabdallah, Walid Hdidi (2017)

Kybernetika

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For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers ${(𝒰_{R})}_{R > 0}$ with increasing regions of attraction ${(Ω_{R})}_{R > 0}$ is that, when the region of attraction $Ω_{R}$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is...

Besov spaces on spaces of homogeneous type and fractals

Dachun Yang (2003)

Studia Mathematica

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Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces $B_{p q}^{s} (Γ)$ defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.

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...