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Stabilité et commande de systèmes décrits par des multimodèles : Approche LMI

Abstract : This thesis deals with the issue of stability and stabilisation of nonlinear systems in multiple model approach. Our study is exclusively based on the second Lyapunov method and its formulation in Linear Matrix Inequality (LMI) form. It carried out around two axes: the first one deals with the quadratic stability and the second treats the non quadratic case. In the quadratic case, we derive sufficient stability conditions by using the properties of M-matrices. The construction of multiple observers in the case of non measurable decision variables and also with unknown entries is then studied. A non linear output feedback control law is also proposed. Two techniques to synthesis this control law are proposed. The first one is based on a convex formulation. The second technique use the transformation of the non convex problem of synthesis into a cone complementarity problem. To reduce the conservativness of the quadratic method, two non quadratic types of Lyapunov function are considered : the polyquadratic Lyapunov function and the piecewise quadratic function. Using the S-procedure, the stability conditions are derived in LMI form. These results led to reduce considerably the conservatism of the quadratic method. They allow to consider interesting extensions to design state/output controller and multiple observer. The obtained conditions are bilinear in the variables of synthesis. LMI formulations under rank constraint or by using linearisation's algorithms are proposed.
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Contributor : Mohammed Chadli <>
Submitted on : Monday, February 9, 2004 - 6:45:59 PM
Last modification on : Friday, October 23, 2020 - 8:38:03 AM
Long-term archiving on: : Friday, April 2, 2010 - 7:27:03 PM


  • HAL Id : tel-00004605, version 1



Mohammed Chadli. Stabilité et commande de systèmes décrits par des multimodèles : Approche LMI. Automatique / Robotique. Institut National Polytechnique de Lorraine - INPL, 2002. Français. ⟨tel-00004605⟩



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