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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

34K20 Stability theory of functional-differential equations