Mulyukov, M. V. On factorization of the characteristic quasipolynomial of a system of linear differential equations with delay. (English. Russian original) Zbl 1287.34060 Russ. Math. 57, No. 9, 31-36 (2013); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2013, No. 9, 38-44 (2013). Summary: We establish a factorization criterion for the characteristic quasipolynomial of a system of two linear autonomous differential equations with delay. On the base of this criterion we obtain several criteria for asymptotic stability. Cited in 2 Documents MSC: 34K20 Stability theory of functional-differential equations 34K06 Linear functional-differential equations Keywords:system with delay; factorization of quasipolynomial; asymptotic stability PDFBibTeX XMLCite \textit{M. V. Mulyukov}, Russ. Math. 57, No. 9, 31--36 (2013; Zbl 1287.34060); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2013, No. 9, 38--44 (2013) Full Text: DOI References: [1] J. Hale Theory of Functional Differential Equations (Springer-Verlag, New York, 1977; Mir, Moscow, 1984). · Zbl 0352.34001 [2] N. V. Azbelev and P. M. Simonov, Stability of Solutions of Ordinary Differential Equations (Permsk. Univ., Perm, 2001) [in Russian]. [3] N. V. Azbelev and P. M. Simonov, Stability of Equations with Delay, Izv. Vyssh. Uchebn. Zaved. Mat., No. 6, 3–15 (1997) [RussianMathematics (Iz. VUZ) 41 (6), 1–14 (1997)]. · Zbl 0910.34063 [4] N. V. Azbelev, V. P. Maksimov, and N. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations (Nauka, Moscow, 1991) [in Russian]. · Zbl 0725.34071 [5] R. Bellman and K. L. Cooke Differential-Difference Equations (Acad. Press, New York, London, 1963; Mir, Moscow, 1967). [6] R. Horn and C. Johnson, Matrix Analysis (Cambridge University Press, New York, 1985; Mir, Moscow, 1989). · Zbl 0576.15001 [7] Yu. A. Bakhturin, Basic Structures of Modern Algebra (Nauka, Moscow, 1990) [in Russian]. · Zbl 0707.00001 [8] Yu. A. Alpin and N. A. Koreshkov, ”On the Simultaneous Triangulability of Matrices,” Matem. Zametki 68(5), 648–652 (2000). [9] F. R. Gantmaher, The Theory of Matrices (AMS Chelsea Publ., 1958; Nauka, Moscow, 1967). [10] M. M. Postnikov, Stable Polynomials, 2nd Ed. (Editorial URSS, Moscow, 2004) [in Russian]. [11] A. A. Andronov and A. T. Maier, ”The Simplest Linear Systems with Retardation,” Avtomatika i Telemekhanika 7(2, 3), 95–106 (1946). · Zbl 0061.20202 [12] A. I. Kir’yanen, Stability of Systems with Delay and Their Applications (S.-Peterburg Univ., St.-Petersburg, 1994) [in Russian]. [13] T. Khokhlova, M. Kipnis, and V. Malygina, ”The Stability Cone for a Delay Differential Matrix Equation,” Appl. Math. Lett. 24(5), 742–745 (2011). · Zbl 1229.34114 [14] A. N. Bykova, ”Investigation in the First Approximation of Stability of Systems of Two Nonlinear Differential Equations with Delay,” Candidate’s Dissertation in Mathematics and Physics (Cheboksary, 2002). 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.