On the uniform asymptotic stability for a linear integro-differential equation of Volterra type (Q852821)

The paper deals with the following linear integro-differential equation of Volterra type: \[ \dot{x}(t) = a x(t) - b \int_{t-h}^t x(s) ds, \] with \(a, b\) real numbers and \(h>0\). The authors consider here only the case of \(a>0\), and study the uniform asymptotic stability of the zero solution to this equation. By using the root analysis of the characteristic equation, a necessary and sufficient condition for asymptotic stability is proved.