On stability of linear delay differential equations under Perron’s condition. (English) Zbl 1217.34117

Summary: The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.


34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations
Full Text: DOI


[1] O. Perron, “Die stabilitätsfrage bei differentialgleichungen,” Mathematische Zeitschrift, vol. 32, no. 1, pp. 703-728, 1930. · JFM 56.1040.01
[2] R. Bellman, “On an application of a Banach-Steinhaus theorem to the study of the boundedness of solutions of non-linear differential and difference equations,” Annals of Mathematics, vol. 49, pp. 515-522, 1948. · Zbl 0031.39902
[3] J. Kloch, “An illustrative example for the Perron condition,” Annales Polonici Mathematici, vol. 35, no. 1, pp. 11-14, 1978. · Zbl 0366.34006
[4] R. Reissig, “A Perron-like stability criterion for linear systems,” Archiv der Mathematik, vol. 34, no. 1, pp. 53-59, 1980. · Zbl 0414.34055
[5] A. Halanay, Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, NY, USA, 1966. · Zbl 0144.08701
[6] M. U. Akhmet, J. Alzabut, and A. Zafer, “Perron’s theorem for linear impulsive differential equations with distributed delay,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 204-218, 2006. · Zbl 1101.34065
[7] A. Anokhin, L. Berezansky, and E. Braverman, “Exponential stability of linear delay impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 193, no. 3, pp. 923-941, 1995. · Zbl 0837.34076
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.