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Systèmes tolérant aux défauts : analyse et synthèse stochastiques

Abstract : Despite the evident interaction between FDI and reconfiguration algorithms, it is true that the research on FDI and reconfiguration methods has often evolved separately, certainly because of the difficulty of each of these problems. The main contribution of this work is to use a mathematical model that includes in the same analysis framework the FDI and reconfiguration algorithms. Such a model belongs to the class of Markovian jump linear systems. In this class of systems, two random processes are defined: the first represents system components failures and the second represents the FDI process. The first problematic considered in this thesis is related to the synthesis of output feedback controllers that stochastically stabilize this class of systems subject to Brownian motion. The developed results are based essentially on Lyapunov theory and Supermartingale notion. The different synthesis conditions are formulated as nonlinear matrix inequalities problematic. Noncovex optimization algorithms were then proposed to solve these conditions. The second problematic addressed in this work concerns the multi-objective control of this class of Markovian jump systems. The specifications and objectives under consideration include stochastic stability, H_{2} and H_{infinity} performances. Output feedback controllers synthesis conditions were also proposed in term of LMI, BMI and NLMI. Finally, we have addressed the discrete-time counterpart and proposed H_{2}/H_{infinity} synthesis conditions. The developed results were applied to the problematic of control of networked systems subject to delays, packet loss and failures.
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Contributor : Samir Aberkane <>
Submitted on : Monday, June 4, 2007 - 11:20:05 AM
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  • HAL Id : tel-00151379, version 1



Samir Aberkane. Systèmes tolérant aux défauts : analyse et synthèse stochastiques. Automatique / Robotique. Université Henri Poincaré - Nancy I, 2006. Français. ⟨tel-00151379⟩



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