An application of the second Lyapunov method to stability investigation of differential equations with deviations

Denis Khusainov

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 1, page 127-142
  • ISSN: 0044-8753

Abstract

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The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides.

How to cite

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Khusainov, Denis. "An application of the second Lyapunov method to stability investigation of differential equations with deviations." Archivum Mathematicum 034.1 (1998): 127-142. <http://eudml.org/doc/248184>.

@article{Khusainov1998,
abstract = {The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides.},
author = {Khusainov, Denis},
journal = {Archivum Mathematicum},
keywords = {Stability; Lyapunov functional; asymptotic stability; stability; Lyapunov functional; asymptotic stability},
language = {eng},
number = {1},
pages = {127-142},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An application of the second Lyapunov method to stability investigation of differential equations with deviations},
url = {http://eudml.org/doc/248184},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Khusainov, Denis
TI - An application of the second Lyapunov method to stability investigation of differential equations with deviations
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 1
SP - 127
EP - 142
AB - The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides.
LA - eng
KW - Stability; Lyapunov functional; asymptotic stability; stability; Lyapunov functional; asymptotic stability
UR - http://eudml.org/doc/248184
ER -

References

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  12. D. Ya. Khusainov A. G. Zhuykova, Stability Estimations for Non-Linear Control Systems with Delay Argument, Institute of Mathematics, Academy of Science of Ukraine, (preliminary edition) 1988 (Russian). (1988) 
  13. D. Ya. Khusainov A. V. Shatyrko, Lyapunov Function Method for Investigation of Differential-Functional System Stability, Kiev University Press, Kiev 1997 (Russian). (1997) MR1486825
  14. D. Ya. Khusainov V. F. Davidov, Solution estimates of quadratic systems with delay, Functional Differential Equations, Israel Seminar, vol. 3 3–4, (1996), 345–356. (1996) MR1459316
  15. D. Ya. Khusainov E. E. Shevelenko, Investigation of differential systems with rational right-hand side, Ukrainian Mathematical Journal, vol. 47 1, (1995), 1292–1299 (Russian). (1995) MR1368138
  16. D. Ya. Khusainov E. E. Shevelenko, Investigation of rational systems with delay, Differential Equations, vol. 31 1, (1995), 175–177 (Russian). (1995) MR1369871

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