Pole Placement of Positive Systems via Perron Root

Abstract

This paper is concerned with pole placement of a positive system whose states take nonnegative values whenever the initial states and inputs are nonnegative. Since assigning the poles of a positive system to any desirable values with preserving its nonnegativity is not possible, Perron root based pole assignability is introduced as a counterpart of standard pole assignability. Then a necessary and sufficient condition of the assignability is given as a linear programming form. A state feedback gain which achieves the pole assignment is also derived.