On the delay-independent stability of a delayed differential equation of 1st order (Q920275)

This paper deals with the delayed differential equation \(\dot x(t)=ax(t)+bx(t-\tau (t)),\) where x(t): \({\mathbb{R}}^+\to {\mathbb{R}}\), a and b are real constants, \(\tau\) (t) is a piecewise continuous real scalar function satisfying \(0\leq \tau (t)\leq \tau_ 0\). A necessary and sufficient condition on a, b and \(\tau_ 0\) for the global asymptotic stability of the differential equation is derived.