Estimation of linear positive systems with unknown time-varying delays

This paper considers the estimation problem for linear positive systems with time-varying unknown delays. Similar to set-valued estimation approaches, we provide a confident region within which the trajectory of the observed positive system always evolves. Guaranteed upper and lower estimates for the instantaneous states are characterized by means of a special kind of extended Luenberger-type interval observer. We provide constructive conditions for its existence and establish the asymptotic convergence of its associated interval error. In addition, we give an LP-based method which allows one to construct the proposed interval observer solely from the data of the system.