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Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques

Leila Ouksel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Dans ce travail, nous donnons une estimation logarithmique des données de la solution u, d'un problème hyperbolique avec condition aux limites de type Neumann, par la trace de u restreinte à un ouvert du bord, pendant un temps suffisamment grand qui nous permet d'estimer la fonction de coût de ce problème.

Infinite-dimensional Sylvester equations: Basic theory and application to observer design

Zbigniew Emirsajłow (2012)

International Journal of Applied Mathematics and Computer Science

This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems and control theory where Sylvester equations widely appear, and for this reason we intend to give a mathematically...

Integrated design of observer based fault detection for a class of uncertain nonlinear systems

Wei Chen, Abdul Q. Khan, Muhammmad Abid, Steven X. Ding (2011)

International Journal of Applied Mathematics and Computer Science

Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the...

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