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Stable systems with two delays. (English. Russian original) Zbl 0906.93049

J. Comput. Syst. Sci. Int. 36, No. 2, 190-196 (1997); translation from Izv. Akad. Nauk, Teor. Sist. Upr. 1997, No. 2, 34-40 (1997).
The paper is devoted to second-order linear autonomous equations with two constant delays. The corresponding quasipolynomial \[ z^2+z+1=c [\exp(-a_1 z)+ \exp(-z a_2)] \] with constants \(c, a_1>0, a_2>0\) is investigated. The possible directions of stable rays are defined. In addition, it is proved that the set of stable rays is finite.

MSC:

93D20 Asymptotic stability in control theory
34K20 Stability theory of functional-differential equations
93C80 Frequency-response methods in control theory
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