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Interconnection of stability in sense of Zhukovsky with another stability notions in topologic dynamic

Keywords:

О.V. Druzhinina, A.A. Shestakov


The problem of stability in the sense of N.E. Zhukovsky for continious nonlinear dynamical system is considered in the paper. New conditions of stability in the sense of Zhukovsky are obtained by the aid of notion of pseudoperiodical stability. The interconnection of notion of stability in the sense of Zhukovsky with another stability notions of topological dynamics is characterized. Obtained stability conditions can be used in problems of stability and chaotic behavior of technical systems, in problems of safety of transport systems and in mathematical control theory.
References:

  1. Nemy'czkij V.V., Stepanov V.V. Kachestvennaya teoriya differenczial'ny'x uravnenij. M.: Gostexizdat. 1949.
  2. Barbashin E.A. Metod sechenij v teorii dinamicheskix sistem. Minsk: Nauka i texnika. 1979.
  3. Sibirskij K.S. Vvedenie v topologicheskuyu dinamiku. Kishinev: AN  MSSR. 1975.
  4. Kozlov V.V., Furta S.D. Asimptotiki reshenij sil'no nelinejny'x sistem differenczial'ny'x uravnenij. M.: MGU. 1996.
  5. Leonov G.A. Xaoticheskaya dinamika i klassicheskaya teoriya ustojchivosti dvizheniya. Moskva–Izhevsk: In-t komp'yuterny'x issledovanij. 2006.
  6. Ding C., Soriano J.M. Uniformly asymptotically Zhukovskij stable orbits // Computers Math. Appl. 2005. V. 49. P. 81–84.
  7. Druzhinina O.V., Shestakov A.A. O soxranenii svojstva asimptoticheskoj prochnosti v smy'sle Zhukovskogo integral'nogo mnozhestva pri vozmushheniyax nelinejnogo differenczial'nogo uravneniya // Doklady' RAN. 2002. T. 384. № 1. S. 52–56.
  8. Druzhinina O.V., Shestakov A.A. O predel'ny'x svojstvax asimptoticheski ustojchivy'x po Lyapunovu i asimptoticheski prochny'x po Zhukovskomu traektorij dinamicheskix sistem // Doklady' RAN. 2006. T. 409. № 2. S. 185–190.
  9. Shestakov A.A., Druzhinina O.V. Final'ny'e svojstva asimptoticheski prochny'x i fazovo asimptoticheski ustojchivy'x traektorij i konechnomerny'x dinamicheskix potokov // Izv. RAEN. Differencz. uravneniya. 2006. № 11. S. 251–255.
  10. Druzhinina O.V. Metody' analiza ustojchivosti i dinamicheskoj prochnosti traektorij nelinejny'x differenczial'ny'x sistem. M.: VC RAN, 2008.
  11. Druzhinina O.V. Ustojchivost' i stabilizacziya po Zhukovskomu dinamicheskix sistem. M.: Knizhny'j dom «Librokom»/ URSS. 2013.
  12. Druzhinina O.V., Shestakov A.A. O rasshirenii ponyatiya orbital'noj ustojchivosti traektorij dinamicheskoj sistemy' // Doklady' RAN. 2001. T. 377. № 5. S. 621–625.
  13.  Druzhinina O.V. Priznaki asimptoticheskoj prochnosti i neprochnosti dvizheniya dinamicheskoj sistemy' // Doklady' RAN. 1997. T. 355. № 4. S. 476–478.
  14.  Druzhinina O.V. Issledovanie prochnosti po Zhukovskomu traektorij gladkix dinamicheskix sistem s pomoshh'yu funkczij Lyapunova // Doklady' RAN. 1998. T. 362. № 2. S. 198–201.
  15.  Druzhinina O.V. O prochnosti v smy'sle Zhukovskogo traektorij nekotory'x sistem nebesnoj mexaniki // Doklady' RAN. 2002. T. 384. № 2. S. 188–192.

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