An analytic stability test for a certain class of distributed parameter systems with a distributed lag

The aim of this note is to apply an algebraic test such as the Hurwitz or the Routh, or the Hermite method to a certain class of distributed parameter systems with a distributed lag. A characteristic equation of such a system is truncated according to Rouché\´s theorem to determine a range of adjustable parameter for which the truncated system and the system with a distributed lag are both input-output stable. An illustrative example is included.