Design of positive linear observers for linear compartmental systems

A positive system is a dynamic system whose trajectory remains in the nonnegative orthant of the state space if it is originated from the orthant. The observer design problem for compartmental systems which are also positive systems is studied. At first, a necessary and sufficient condition on the existence of a positive observer is provided which corrects a previous result in the literature. By relaxing the observer structure, we propose a new design method of positive linear observer for single output systems which requires only the detectability condition. Academic examples are provided to illustrate the theory.