Existence Conditions and a Constructive Design of Positive Linear Observers for Positive Linear Systems

Positive systems are dynamic systems whose trajectories remain in the nonnegative orthant of the state space if originated from the orthant. The relation between the spectrum of the system matrix and the existence of positive linear observers, which employ a coordinate transformation, is investigated. Necessary conditions for the existence of positive observers are provided. The paper also provides a constructive design method for a class of systems whose system matrix has real and distinct eigenvalues