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
2 BIOCORE - Biological control of artificial ecosystems

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.

Mots clés: Positive system; interval observer; Metzler matrix

Domaines: Automatique

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, 2021, pp.1-1. ⟨10.1109/TAC.2021.3123245⟩. ⟨hal-03533716⟩