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Avtomatika i Telemekhanika, 2006, Issue 9, Pages 3–14 (Mi at1230)  
This article is cited in 20 scientific papers (total in 20 papers)

Deterministic Systems

On stability of the solutions of a class of nonlinear delay systems

A. Yu. Aleksandrov, A. P. Zhabko

Saint-Petersburg State University
Full-text PDF (219 kB) Citations (20)
References:
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Abstract: Consideration was given to a class of systems of nonlinear differential equations with retarded argument. It was assumed that in the absence of delay the zero solutions of the systems under study are asymptotically stable. Using the method of Lyapunov functions in the form of B. S. Razumikhin, it was proved that if the right-hand sides of these equations are free of the linear terms relative to the phase variables, then the asymptotic stability is retained for any delay.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 06.10.2005
English version:
Automation and Remote Control, 2006, Volume 67, Issue 9, Pages 1355–1365
DOI: https://doi.org/10.1134/S0005117906090013
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ks, 02.30.Yy
Language: Russian
Citation: A. Yu. Aleksandrov, A. P. Zhabko, “On stability of the solutions of a class of nonlinear delay systems”, Avtomat. i Telemekh., 2006, no. 9, 3–14; Autom. Remote Control, 67:9 (2006), 1355–1365
Citation in format AMSBIB
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\jour Avtomat. i Telemekh.
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\yr 2006
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\crossref{https://doi.org/10.1134/S0005117906090013}
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Linking options:
  • https://www.mathnet.ru/eng/at1230
  • https://www.mathnet.ru/eng/at/y2006/i9/p3
    • This publication is cited in the following 20 articles:
    1. Alexander Aleksandrov, Natalya Andriyanova, “Stability analysis of Lur'e indirect control systems with time delay and multiple nonlinearities”, Int. J. Dynam. Control, 11:6 (2023), 3074  crossref
    2. Aleksandrov A., Andriyanova N., Efimov D., “Stability Analysis of Persidskii Time-Delay Systems With Synchronous and Asynchronous Switching”, Int. J. Robust Nonlinear Control, 32:6 (2022), 3266–3280  crossref  isi  scopus
    3. Alexander Aleksandrov, Denis Efimov, “Averaging method for the stability analysis of strongly nonlinear mechanical systems”, Automatica, 146 (2022), 110576  crossref
    4. V. V. Provotorov, S. M. Sergeev, A. A. Part, “Solvability of hyperbolic systems with distributed parameters on the graph in the weak formulation”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 15:1 (2019), 107–117  mathnet  crossref  elib
    5. Aleksandrov A.Yu., Aleksandrova E.B., “Delay-Independent Stability Conditions For a Class of Nonlinear Difference Systems”, J. Frankl. Inst.-Eng. Appl. Math., 355:7 (2018), 3367–3380  crossref  mathscinet  zmath  isi  scopus
    6. Aleksandrov A.Yu. Aleksandrova E.B. Tikhonov A.A., “On the Monoaxial Stabilization of a Rigid Body Under Vanishing Restoring Torque”, Eighth Polyakhov'S Reading, AIP Conference Proceedings, 1959, ed. Kustova E. Leonov G. Morosov N. Yushkov M. Mekhonoshina M., Amer Inst Physics, 2018, UNSP 080001-1  crossref  mathscinet  isi  scopus
    7. Aleksandrov A.Yu. Zhabko A.P. Chen Y., “Stability Analysis of Gyroscopic Systems With Delay Via Decomposition”, Eighth Polyakhov'S Reading, AIP Conference Proceedings, 1959, ed. Kustova E. Leonov G. Morosov N. Yushkov M. Mekhonoshina M., Amer Inst Physics, 2018, UNSP 080002-1  crossref  isi  scopus
    8. Alexander Aleksandrov, Yangzhou Chen, 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy's Conference) (STAB), 2018, 1  crossref
    9. V. V. Provotorov, E. N. Provotorova, “Optimal control of the linearized Navier–Stokes system in a netlike domain”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:4 (2017), 431–443  mathnet  crossref  elib
    10. Ekimov A.V., Balykina Yu.E., Svirkin M.V., “Analysis of Attainability Sets of Bilinear Control Systems”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 170012-1  crossref  mathscinet  isi  scopus
    11. Aleksandrov A.Yu. Aleksandrova E.B., “Convergence Conditions For Some Classes of Nonlinear Systems”, Syst. Control Lett., 104 (2017), 72–77  crossref  mathscinet  zmath  isi  scopus
    12. Talebi S., Ataei M., Ekramian M., “Guaranteed Interval of Delay For a Class of Non-Linear Control Systems”, Trans. Inst. Meas. Control, 38:3 (2016), 364–369  crossref  isi  scopus
    13. Srinivasan V., Sukavanam N., “Asymptotic Stability and Stabilizability of Nonlinear Systems With Delay”, ISA Trans., 65 (2016), 19–26  crossref  isi  scopus
    14. Sayed M., Mousa A.A., Alzaharani D.Y., “Non-Linear Time Delay Saturation Controller For Reduction of a Non-Linear Vibrating System Via 1:4 Internal Resonance”, J. Vibroeng., 18:4 (2016), 2515–2536  crossref  isi  elib  scopus
    15. S. L. Podvalnyi, V. V. Provotorov, “Startovoe upravlenie parabolicheskoi sistemoi s raspredelennymi parametrami na grafe”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2015, no. 3, 126–142  mathnet  elib
    16. Wang M., Chen B., “Stability Analysis For a Class of Delayed Neural Networks With Nonlinear Homogeneous Activation Functions”, 2015 Sixth International Conference on Intelligent Control and Information Processing (Icicip), IEEE, 2015, 30–35  crossref  isi  scopus
    17. Malafeyev O.A., Nemnyugin S.A., Ivaniukovich G.A., “Stochastic Models of Social-Economic Dynamics”, 2015 International Conference “Stability and Control Processes” in Memory of V.i. Zubov (Scp), eds. Petrosyan L., Zhabko A., IEEE, 2015, 483–485  isi
    18. Oleg A. Malafeyev, Sergey A. Nemnyugin, Georgy A. Ivaniukovich, 2015 International Conference “Stability and Control Processes” in Memory of V.I. Zubov (SCP), 2015, 483  crossref
    19. Aleksandrov A.Yu., Hu G.-D., Zhabko A.P., “Delay-Independent Stability Conditions For Some Classes of Nonlinear Systems”, IEEE Trans. Autom. Control, 59:8 (2014), 2209–2214  crossref  mathscinet  zmath  isi  elib  scopus
    20. Aleksandrov A.Yu., Zhabko A.P., “Delay-Independent Stability of Homogeneous Systems”, Appl. Math. Lett., 34 (2014), 43–50  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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