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Stability of neutral delay-differential systems: Boundary criteria. (English) Zbl 0913.34060
For linear neutral delay differential equations of the form $\dot{x}(t)=Ax(t)+Bx(t-\tau)+C\dot{x}(t-\tau),$ where $$x:{\mathbb{R}}_+\to{\mathbb{R}}^n$$ is an unknown function, $$A$$, $$B$$ and $$C$$ are constant $$n\times n$$-matrices and $$\tau=\text{ const}>0$$, a series of delay dependent asymptotical stability criteria are given. The criteria are based on the evaluation of a real-valued function on the boundary of a rectangle in the complex plane.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations 34K10 Boundary value problems for functional-differential equations
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##### References:
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