Sufficient conditions for the stability of linear periodic impulsive differential equations

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Дәйексөз келтіру

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Аннотация

Abstract linear periodic impulsive differential equations are considered. The impulse effect instants are assumed to satisfy the average dwell-time condition (the ADT condition). The stability problem is reduced to studying the stability of an auxiliary abstract impulsive differential equation. This is a perturbed periodic impulsive differential equation, which considerably simplifies the construction of a Lyapunov function. Sufficient conditions for the asymptotic stability of abstract linear periodic impulsive differential equations are obtained. It is shown that the ADT conditions lead to less conservative dwell-time estimates guaranteeing asymptotic stability. Bibliography: 24 titles.

Авторлар туралы

Vladyslav Bivziuk

University of Illinois at Urbana-Champaign

Vitalii Slyn'ko

Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine; Julius-Maximilians-Universität Würzburg

Email: vitstab@ukr.net
Doctor of physico-mathematical sciences, Head Scientist Researcher

Әдебиет тізімі

  1. C. Briat, A. Seuret, “A looped-functional approach for robust stability analysis of linear impulsive systems”, Systems Control Lett., 61:10 (2012), 980–988
  2. C. Briat, “Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems”, Nonlinear Anal. Hybrid Syst., 24 (2017), 198–226
  3. А. И. Двирный, В. И. Слынько, “Применение прямого метода Ляпунова к исследованию устойчивости решений систем дифференциальных уравнений с импульсным воздействием”, Матем. заметки, 96:1 (2014), 22–35
  4. V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of impulsive differential equations, Ser. Modern Appl. Math., 6, World Sci. Publ., Teaneck, NJ, 1989, xii+273 pp.
  5. А. М. Самойленко, Н. А. Перестюк, Дифференциальные уравнения с импульсным воздействием, Вища школа, Киев, 1987, 288 с.
  6. Xinzhi Liu, A. Willms, “Stability analysis and applications to large scale impulsive systems: a new approach”, Canad. Appl. Math. Quart., 3:4 (1995), 419–444
  7. A. O. Ignatyev, “On the stability of invariant sets of systems with impulse effect”, Nonlinear Anal., 69:1 (2008), 53–72
  8. А. И. Двирный, В. И. Слынько, “Об устойчивости по нелинейному квазиоднородному приближению дифференциальных уравнений с импульсным воздействием”, Матем. сб., 205:6 (2014), 109–138
  9. C. Briat, “Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints”, Automatica, 49:11 (2013), 3449–3457
  10. В. И. Слынько, “Об условиях устойчивости линейных импульсных систем с запаздыванием”, Прикл. мех., 41:6 (2005), 130–138
  11. V. I. Slyn'ko, O. Tunç, V. O. Bivziuk, “Application of commutator calculus to the study of linear impulsive systems”, Systems Control Lett., 123 (2019), 160–165
  12. D. Chatterjee, D. Liberzon, “Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions”, SIAM J. Control Optim., 45:1 (2006), 174–206
  13. Jianquan Lua, D. W. C. Ho, Jinde Cao, “A unified synchronization criterion for impulsive dynamical networks”, Automatica, 46:7 (2010), 1215–1221
  14. Xiaodi Li, Peng Li, Qing-guo Wang, “Input/output-to-state stability of impulsive switched systems”, Systems Control Lett., 116 (2018), 1–7
  15. S. Dashkovskiy, A. Mironchenko, “Input-to-state stability of nonlinear impulsive systems”, SIAM J. Control Optim., 51:3 (2013), 1962–1987
  16. M. A. Müller, D. Liberzon, “Input/output-to-state stability and state-norm estimators for switched nonlinear systems”, Automatica, 48:9 (2012), 2029–2039
  17. Ticao Jiao, Wei Xing Zheng, Shengyuan Xu, “Stability analysis for a class of random nonlinear impulsive systems”, Internat. J. Robust Nonlinear Control, 27:7 (2017), 1171–1193
  18. W. Magnus, “On the exponential solution of differential equations for a linear operator”, Comm. Pure Appl. Math., 7 (1954), 649–673
  19. A. A. Agrachev, D. Liberzon, “Lie-algebraic stability criteria for switched systems”, SIAM J. Control Optim., 40:1 (2001), 253–269
  20. A. A. Agrachev, Yu. Baryshnikov, D. Liberzon, “On robust Lie-algebraic stability conditions for switched linear systems”, Systems Control Lett., 61:2 (2012), 347–353
  21. С. А. Кутепов, “Абсолютная устойчивость билинейных систем с компактным фактором Леви”, Кибернетика и вычислительная техника, 62 (1984), 28–33
  22. D. Liberzon, J. P. Hespanha, A. S. Morse, “Stability of switched systems: a Lie-algebraic condition”, Systems Control Lett., 37:3 (1999), 117–122
  23. V. Slyn'ko, C. Tunç, “Stability of abstract linear switched impulsive differential equations”, Automatica, 107 (2019), 433–441
  24. Ю. Л. Далецкий, М. Г. Крейн, Устойчивость решений дифференциальных уравнений в банаховом пространстве, Наука, М., 1970, 534 с.

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© Bivziuk V.O., Slyn'ko V.I., 2019

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