A reduction method and qualitative analysis of dynamic systems: II

  • S. N. Vasil’ev
Control in Deterministic Systems

Abstract

In the first part of this series, the method of reduction was proposed as a logical engine for hypotheses formulation as the development of the well-known algorithms of the comparison method. In this part, its application for the qualitative analysis of different properties of dynamical systems given in form of motion systems, differential equations, and automata models with various depths of delay is demonstrated.

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References

  1. 1.
    S. N. Vasil’ev, “A Method of Reduction and Qualitative Analysis of Dynamical Systems I,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 1 (2006) [Comp. Syst. Sci. 45 (1), (2006)].Google Scholar
  2. 2.
    F. L. Chernous’ko, L. D. Akulenko, and B. N. Sokolov, Control of Oscillations (Nauka, Moscow, 1980) [in Russian].Google Scholar
  3. 3.
    A. V. Lakeev, Candidate’s Dissertation in Mathematics and Physics (IDSTU SO RAN, Irkutsk, 1987).Google Scholar
  4. 4.
    V. M. Matrosov, S. N. Vasil’ev, R. I. Kozlov, et al., Algorithms of Theorem Proving of the Method of Lyapunov Vector Functions (Nauka, Novosibirsk, 1981) [in Russian].Google Scholar
  5. 5.
    S. N. Vasil’ev, “The Comparison Method in Systems Analysis I–IV,” Differ. Uravn. Ikh Primen. 17(19) (1981); 17 (11) (1981); 18 (2) (1982); 18 (6) (1982).Google Scholar
  6. 6.
    A. N. Michel, K. Wang, and B. Ho, Qualitative Theory of Dynamical Systems: The Role of Stability Preserving Mappings (Marcel Dekker, New York, Basel, 2001).Google Scholar
  7. 7.
    K. S. Sibirskii, Introduction to Topological Dynamics (RIO AN MSSR, Chisinau, 1970) [in Russian].Google Scholar
  8. 8.
    V. I. Zubov, The Lyapunov Methods and Their Application (Leningr. Gos. Univ., Leningrad, 1957) [in Russian].Google Scholar
  9. 9.
    E. Goles and S. Martinez, Neural and Automata Networks (Kluwer, 1990).Google Scholar
  10. 10.
    S. N. Vasil’ev, “Control of the Dynamics of Behavior of Automaton,” in Proceedings of 11th International Baikal Workshop, Plenary Sessions, Irkutsk, Russia, 1998 [in Russian].Google Scholar
  11. 11.
    C. Chang and R. C. Lee, Symbolic Logic and Mechanical Theorem Proving (Academic, 1973; Nauka, Moscow, 1983).Google Scholar
  12. 12.
    S. N. Vasil’ev, A. K. Zherlov, E. A. Fedosov, et al., Intelligent Control for Dynamical Systems (FIZMATLIT, Moscow, 2000) [in Russian].Google Scholar
  13. 13.
    S. N. Vasil’ev, “A Method for Synthesis of the Conditions of Deducibility of Horn and Some Other Formulas,” Sib. Mat. Zh. 38(5) (1997).Google Scholar

Copyright information

© Pleiades Publishing, Inc 2006

Authors and Affiliations

  • S. N. Vasil’ev
    • 1
  1. 1.Institute for Systems Dynamics and Control Theory, Siberian DivisionRussian Academy of SciencesIrkutskRussia

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