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When is a Matrix of Dimension 3 Similar to a Metzler Matrix ? Application to Interval Observer Design

Frederic Mazenc 1 Olivier Bernard 2
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
Inria Saclay - Ile de France, L2S - Laboratoire des signaux et systèmes
2 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche, INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : A simple necessary and sufficient condition ensuring that a real matrix of dimension 3 is similar to a Metzler matrix is exhibited. When this condition is satisfied, a construction of the transfer matrix is given. This construction is used to design an interval observer for a family of continuous-time systems. An example is provided with interval observer design for the so-called love dynamics in the case of limit cycles.
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Submitted on : Friday, January 21, 2022 - 2:51:38 PM
Last modification on : Sunday, May 1, 2022 - 3:16:28 AM
Long-term archiving on: : Friday, April 22, 2022 - 6:47:57 PM

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Frederic Mazenc, Olivier Bernard. When is a Matrix of Dimension 3 Similar to a Metzler Matrix ? Application to Interval Observer Design. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2021, pp.1-1. ⟨10.1109/TAC.2021.3123245⟩. ⟨hal-03533716⟩

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