I. Introduction
Positive systems can be characterized either in terms of their input-output behavior (nonnegative output response to nonnegative inputs), or by the input-state-output behavior (nonnegative state and output responses to nonnegative inputs and initial states) [14], [19], [24]. Positive systems appear in applications where the input, state, and output variables represent intrinsically positive quantities, such as populations, consumption of goods, densities of chemical species, and so on. In the continuous-time framework, a relevant application area for positive systems is that of compartmental systems (see e.g., [1], [5], [14], [15], [20]). In this subject, the positive realization problem consists in finding positive state-space realizations of positive transfer matrices [2], [3], [6], [10], [18]. The issue of the minimality of such positive realizations is investigated in [4], [6], [8], mainly in the discrete-time framework.