Growth estimates and asymptotic stability for a class of differential- delay equation having time-varying delay
Using the technique of Lyapunov functionals the author studies the asymptotic stability of the equation \(\dot x(t)=Ax(t)+Bx(t-h(t))\), where \(x(t)\in\mathbb{R}^ n\). Bounds are derived on the norm of the solution in terms of the behaviour of \(| h'(t)|\) and its average \(a(t)=t^{- 1}\int^ t_ 0| h'(s)| ds\). In particular if \(\liminf_{t\to\infty}a(t)=0\) then each bounded solution \(x\) satisfies \(\liminf_{t\to\infty}| x(t)|=0\).
scientific article; zbMATH DE number 62050