Sur la stabilité et la stabilisation de systèmes non linéaires discrets

Abstract : Our concern in this work is the folowing ithems : 1)stability and stabilization of discrete time systems : the aim is to presente some new results on the stability theory. We give a sufficent condition for stability of discrete time nonlinear systems. We show how to use semi definite function instead of a definite one for the qualitative study of a given system. This approach extends the basic result in Lyapunov theory. The interest of semi definite function than a definite one. We apply the results that we get to the study of the stability (center manifold, cascade systems, the link detectability --stability), and to the feedback stabilisation problems (cascade systems, dissipative systems, stabilization by estimited state feedback,...). These applications show that the use of semi definite Lyapunov functions allows to get a simple and nice proofs. 2) Stabilization of non-autonomuous periodic systems : we give a discrete version of a Krasovski theorem for non-autonomuous periodic systems. This allows us to give a sufficent condition for stabilization of periodic discrete time nonlinear systems. A computation of an explicite time periodic feedback is given. We apply the result to give a systematic way to design time variant feedback for autonomuous discrete time systems that cannot be stabilized via a time invariant continuous feedback. 3)Stabilization of dissipative continuous non affine control systems : we generalise the result of Jurdjevic and Quinn for affine systems to nonaffine control systems in both deterministic and stochastic cases
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Mohamed Bensoubaya. Sur la stabilité et la stabilisation de systèmes non linéaires discrets. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1997. Français. ⟨NNT : 1997METZ040S⟩. ⟨tel-01777223⟩

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