Abstract

We give an extension of the classical Perron-Frobenius theorem to a class of positive quasi-polynomial operators. Then the obtained results are applied to show that delay-independent exponential stability and exponential stability of positive linear delay systems are equivalent, and are characterized by a simple criterion. Next, we show that delay-independent exponential stability radii and exponential stability radii coincide and can be computed via simple formula. Finally, a simple example is given to illustrate the obtained results.