350 rub
Journal Dynamics of Complex Systems - XXI century №4 for 2014 г.
Article in number:
Qualitative analysis and estimation of linearization error for multiply connected dynamical systems
Keywords: multiply connected nonlinear system asymptotical stability estimation of linearization error uniform boundedness technical manipulator
Authors:
O. V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Chief Researcher, Dorodnicyn Computing Center of RAS (Moscow). E-mail: ovdruzh@mail.ru E. V. Shchennikova - Dr.Sc. (Phys.-Math.), Professor, National Research Mordovian State University by the name of N.P. Ogarev (Saransk). E-mail: schennikova8000@yandex.ru
Abstract:
Multiply connected dynamical systems described by nonlinear finite-dimensional differential equations are considered. Conditions of asymptotical stability with respect to one part phase variables and conditions of uniform boundedness with respect to another part phase variables are suggested. Estimation of linearization error is constructed by the aid of Lyapunov vector functions method. The obtained results can be used in problems of analysis of behavior of technical manipulators. In the present paper a constructive method of qualitative analysis of dynamical systems multiply, as well as a method of constructing estimates linearization of these systems. The results obtained are solving problems of correctness of the use of linearized systems in the theory of motion stability of nonlinear systems.
Pages: 20-24
References

 

  1. Zubov V.I. Matematicheskie metody issledovanija sistem avtomaticheskogo regulirovanija. L.: Mashinostroenie. Leningrad. otd. 1974. 336 s.
  2. Aleksandrov A.JU., Platonov A.V. Metod sravnenija i ustojjchivost dvizhenijj nelinejjnykh sistem. SPb.: Izd-vo S.-Peterb. un-ta. 2012. 263 s.
  3. Druzhinina O.V., SHHennikov V.N., SHHennikova E.V. Postroenie ocenki maksimalnogo otklonenija reshenijj nelinejjnojj mnogosvjaznojj sistemy i sootvetstvujushhejj sistemy pervogo priblizhenija // Trudy X Mezhdunar. CHetaevskojj konf. T. 1. Sekcija 1. Analiticheskaja mekhanika. Kazan, 12-16 ijunja 2012 g. Kazan: Izd-vo Kazan. gos. tekhn. un-ta. 2012. S. 143-153.
  4. SHHennikova E.V. Ustojjchivopodobnye svojjstva reshenijj odnojj mnogosvjaznojj sistemy differencialnykh uravnenijj // Matematicheskie zametki. 2012. T. 91. Vyp. 1. S. 136-142.
  5. Druzhinina O.V., SHHennikov V.N., SHHennikova E.V.Uslovija i algoritmy optimalnojj stabilizacii otnositelno chasti peremennykh mnogosvjaznykh nelinejjnykh upravljaemykh sistem // Dinamika slozhnykh sistem. 2012. T. 6. № 3. S. 154-158.
  6. Vukobratovich M., Stokich D. Upravlenie manipuljacionnymi robotami. M.: Nauka. 1985.
  7. Druzhinina O.V., SHHennikov V.N., SHHennikova E.V. Algoritmy optimalnojj stabilizacii programmnogo dvizhenija manipuljacionnojj dinamicheskojj sistemy // Nelinejjnyjj mir. 2012. T. 10. № 12. S. 932-937.
  8. Druzhinina O.V., Masina O.N., SHHennikova E.V. Optimalnaja stabilizacija programmnogo dvizhenija manipuljacionnykh dinamicheskikh sistem // Dinamika slozhnykh sistem. 2011. T. 5. № 3. S. 58-64.
  9. Rosier L. Homogeneous Lyapunov fuction for homogeneous continuous vector field // Syst. Contz. Lett. 1992. V. 19.  № 6. P. 467-473.
  10. Martynjuk A.A., Obolenskijj A.JU. Ob ustojjchivosti avtonomnykh sistem Vazhevskogo // Differencialnye uravnenija. 1980. T.16. № 8. S. 1392-1407.
  11. Masina O.N., Druzhinina O.V. Modelirovanie i analiz ustojjchivosti nekotorykh klassov sistem upravlenija. M.: VC RAN. 2011.
  12. Druzhinina O.V. Ustojjchivost i stabilizacija po ZHukovskomu dinamicheskikh sistem: Teorija, metody i prilozhenija. M.: URSS. 2013. 256 s.