On a class of positive linear differential equations with infinite delay

We give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a Perron–Frobenius type theorem for positive equations. Furthermore, a novel criterion for the exponential asymptotic stability of positive equations is presented. Finally, we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations. A simple example is given to illustrate the obtained results.