Positive observers for continuous time interval positive systems with time-delay

This paper is concerned with the design of positive observers for positive interval systems with time delay. For that, a solution based on LMI programming is provided to the problem of designing observers that ensure guaranteed bounds on the estimated states that are nonnegative whenever the initial conditions are nonnegative. Furthermore, it is revealed that an unstable positive system cannot be positively stabilized without taking into account the positivity of the dynamic errors. We derive then necessary and sufficient conditions for the existence of positive observers and show that the solvability can be decided via LMI (Linear Matrix Inequalities) programming techniques.