Positive observers for linear positive systems in a Hilbert lattice space

Abstract

In this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice of the observer gain and using positive bounded perturbation results. We show in particular that the error of the state estimation converges exponentially to zero. Finally, the main result is applied to an isothermal tubular (bio) reactor model, namely the plug-flow (bio) reactor model. The approach is illustrated by some numerical simulations.