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Investigation of the stability of linear systems of neutral type by the Lyapunov-function method. (English. Russian original) Zbl 0674.34077
Differ. Equations 24, No. 4, 424-431 (1988); translation from Differ. Uravn. 24, No. 4, 613-621 (1988).
Equations of the form $\dot x(t)=D\dot x(t-\tau)+Ax(t)+Bx(t-\tau)$ are considered from the viewpoint of the asymptotic stability of the trivial solution $$x\equiv 0$$ as well as the stability with respect to persistent perturbations by nonlinear terms of the form $$Q(x(t),x(t- \tau),\dot x(t-\tau)).$$ The results are derived via the “degenerate” system $$\dot x(t)=(I-D)^{-1}(A+B)x(t)$$ and its stability properties via the Lyapunov function for this autonomous linear system of ordinary differential equations.
Reviewer: Š.Schwabik

MSC:
 34K20 Stability theory of functional-differential equations