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Exponentially Stable Interval Observers for Linear Systems with Delay.

Frédéric Mazenc 1, 2 Silviu-Iulian Niculescu 2, 1 Olivier Bernard 3
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
3 BIOCORE - Biological control of artificial ecosystems
INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche
Abstract : This paper focuses on the analysis and the design of families of interval observers for linear systems with a point-wise delay. First, it is proved that classical interval observers for systems without delays are not robust with respect to the presence of delays, no matter how small delays are. Next, it is shown that, in general, for linear systems with delay, the classical interval observers endowed with a point-wise delay are unstable. A new type of design of interval observers enabling to circumvent these obstacles is proposed. It provides with framers that incorporate distributed delay terms. The proposed interval observers are assessed through a non-linear biotechnological model.
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Frédéric Mazenc, Silviu-Iulian Niculescu, Olivier Bernard. Exponentially Stable Interval Observers for Linear Systems with Delay.. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (1), pp.286-305. ⟨10.1137/100812124⟩. ⟨hal-00761603⟩

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