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Fault Tolerant Control design for polytopic LPV systems

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Rodrigues M., Theilliol D., Aberkane S., Sauter D.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 1
27-37
EN
This paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both fault-free and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.
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A multi-model approach to Saint-Venant equations: A stability study by LMIs

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Dos Santos Martins V., Rodrigues M., Diagne M.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
539-550
EN
This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.
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