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Stabilisation de systèmes bilinéaires et de systèmes mécaniques

Abstract : This thesis is constituted od two independent parts. The first part is devoted to the feedback stabilization of planar bilinear systems, with a precise description of the closed - loop system from both points of view of phase portrait and convergence rate. The main idea is to adapt the principle of Kalman'spoles assignement for linear systems, to bilinear case under an appropriate assumption. We get a homogeneous system of degree one, formally alike to a classical linear system (with a constant matrix), but whose matrix depends on the state. Fixing the spectrum of this matrix provides a homogeneous feedback of degree zero. Whatever the chosenfixed spectrum may be (two complex conjugate numbers, or two real numbers), we observe a strong similarity of the phase portrait with the one of linear system with the same spectrum, up to a "splitting into two" of the eigendirections for the real case ; in both cases, we get a uniform exponential overestimation of the state norm that is quite identical to the one of the linear case. Endly we deal with the same problem by use of feedbacks laws, that are constant on angular sectors. The second part is devoted to the stabilization, via an observer giving an estimate of the velocity, of a rigid manipulator
Mots-clés : Systèmes linéaires
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Martine Clavier. Stabilisation de systèmes bilinéaires et de systèmes mécaniques. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1995. Français. ⟨NNT : 1995METZ037S⟩. ⟨tel-01777094⟩



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