METHODS FOR STUDYING THE ASYMPTOTIC PROPERTIES AND STABILIZATION OF SOME SYSTEMS WITH LINEAR DELAY

B. G. Grebenshchikov, S. A. Zagrebina, A. B. Lozhnikov

Abstract


Methods for obtaining sufficient conditions of asymptotic
stability and instability for systems of differential equations containing linear delay are proposed.
Based on these conditions, some systems of linear differential equations are investigated, one of them is stabilized over an infinite period of time.


Keywords


asymptotic stability; linear delay; stabilization

Full Text:

PDF

References


Bellman R., Cooke K. Differential-Difference Equations. New York, Academic Press, 1963.

Sesekin A.N., Shlyakhov A.S. On the Stability of Discontinuous Solutions of Bilinear Systems With Impulse Action, Constant and Linear Delays. AIP Conference Proceedings, 2019, vol. 2172, pp. 1-5.

Zhabko A.P., Tihomirov O.G., Chizhova O.N. Stabilization of a Class of Systems With Proportional Delay. Bulletin of St. Petersburg University. Series A. Applied Mathematics. Computer science. Management processes, 2018, vol. 14, issue 2, pp. 165-172. (in Russian) DOI: 10.21638/11702/spbu10.2018.209

Barbashin E.A. Introduction to the Theory of Stability. Moscow, Nauka, 1967. (in Russian)

Elsgolts L.E., Norkin S.B. Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Mathematics in Science and Engineering, 105. New York, Academic Press, 1973.

Grebenshchikov B.G., Novikov S.I. Instability of Systems With Linear Delay Reducible to Singularly Perturbed Ones. Russian Mathematics, 2010, vol. 54, no. 2, pp.1-10.

Grebenshchikov B.G. The First-Approximation Stability of a Nonstationary System With Delay. Russian Mathematics, 2012, vol. 56, no. 2, pp. 29-36. DOI: 10.3103/S1066369X12020041

Grebenshchikov B.G., Lozhnikov A.B. Asymptotic Properties of a Class of Systems with Linear Delay. Differential Equations, 2023, vol. 59, no. 5, pp. 577-590. DOI: 10.1134/S0012266123050014

Halanau A., Wexler D. Teoria Calitativa a Sistemelor cu Impulsuri. Editura Academiei Republiciti Socialiste, Bucarest, 1968.

Furasov V.D. Stability of Motion, Estimates and Stabilization. Moscow, Nauka, 1977. (in Russian)

Grebenshchikov B.G. Stability of Systems With Variable Delay Linearly Dependent on Time. Stability and Nonlinear Oscillations. Collection of Scientific Papers. Sverdlovsk, 1983, pp. 25-34. (in Russian)

Furasov V.D. Stability and Stabilization of Discrete Processes.

Moscow, Nauka, 1982.

Kim A.V., Pimenov V.G. I-Smooth Analysis and Numerical Methods for Solving Functional Differential Equations. Moscow, Izhevsk, Regulyarnaya i khaoticheskaya dinamika, 2004. (in Russian)


Refbacks

  • There are currently no refbacks.


 Save