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Stability criteria of linear neutral systems with distributed delays. (English) Zbl 1251.45006
This paper concerns the stability of linear neutral systems with distributed delay. A bounded half circular region which includes all unstable characteristic roots, is considered. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded half circular region. If there are no characteristic roots on the imaginary axis, the number of unstable characteristic roots can be obtained. Numerical examples are given to illustrate the presented results.

45M10 Stability theory for integral equations
45J05 Integro-ordinary differential equations
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