Positive stabilization of infinite-dimensional linear systems

The main goal of this paper is to give a short tutorial on the positivity and the positive stabilization of infinite dimensional linear systems together with some new points of view and perspectives. Algebraic conditions of positivity for dynamical systems defined on an ordered Banach space whose positive cone has an empty interior are derived. The positive stabilization problem for linear infinite-dimensional systems is also addressed. Sufficient conditions are established to stabilize positively a class of distributed parameter systems, such that the closed loop system is stable and positive.