Design of robust observers for positive delayed interval systems

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. Then, the problem of positive stabilization by dynamic feedback controllers based observer is investigated, taking into account that the positivity of the error signals is necessary to stabilize a positive system and keep it positive at the same time. 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.