This paper addresses the problem of achieving monotonic tracking control for any initial condition (also referred to as global monotonic tracking control). This property is shown to be equivalent to global non-overshooting as well as to global non-undershooting (i.e., non-overshooting and non-undershooting for any initial condition, respectively). The main objective of this paper is to prove that a stable system is globally monotonic if and only if all the rows of the output matrix are left eigenvectors of the space transition matrix. This property allows one to formulate the design of a controller which ensures global monotonic tracking as a convex optimization problem described by a set of Linear Matrix Inequalities (LMIs). (C) 2015 Elsevier Ltd. All rights reserved.