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Theses

Filtrage robuste pour les systèmes stochastiques incertains

Abstract : This memory approaches the synthesis of full and reduced-order H-infinity filters for continuous time stochastic systems with multiplicative noises. The noises considered in the state equation and in the measurement one are Wiener processes.

The stochastic systems studied in this memory are written in the form of an Itô differential equation in which the drift and the diffusion are linear or bilinear. The systems with several multiplicative noises and the systems whose measurements are affected by multiplicative noises are treated in this memory. Finally, the design of reduced-order H-infinity observer-based control for the uncertain stochastic systems is studied.

The performance index considered is the H-infinity criterion from the disturbance signal towards the estimation error signal. The stability retained for these stochastic systems in this work is the exponential mean-square stability.

The method used to find the matrices of the filters is based on the use of the theory of Lyapunov for the stochastic differential equations, the Itô formula and on the resolution of Linear Matrix Inequalities coupled to bilinear constraints which ensure the stability and the performance.
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Contributor : Souheil Halabi <>
Submitted on : Wednesday, January 11, 2006 - 11:56:25 AM
Last modification on : Friday, October 23, 2020 - 8:38:04 AM
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Souheil Halabi. Filtrage robuste pour les systèmes stochastiques incertains. Automatique / Robotique. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10134⟩. ⟨tel-01748164v2⟩

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