Pole-assignment for a class of positive linear systems

Abstract

Positive systems are defined as systems with trajectories entirely in the non-negative orthant whenever the initial state is non-negative. The cohort-type model represents the class of positive linear systems considered here. The method and procedure for pole-assignment of the corresponding closed-loop positive system is proposed. The method is based on inverse eigenspectrum conditions developed for the class of system under consideration and on monomial similarity of non-negative matrices. The relation between controllability and pole-assignment is also studied. Numerical examples illustrating the procedure are provided.