Ukrainian Mathematical Journal

, Volume 44, Issue 8, pp 1047–1051 | Cite as

Stability and controllability of the motion of dynamical systems far off from equilibrium positions

  • M. K. Sparavalo
Brief Communications
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Abstract

We prove theorems that establish the connection between the stability and the controllability of the motion far off from the equilibrium positions and the existence of homogeneous ω-attractors, ω-repellers, and ω-shunts in the extended state space of dynamical systems.

Keywords

Dynamical System State Space Equilibrium Position Extended State Extended State Space 
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Literature cited

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    J. Palis, Jr. and W. de Melo, Geometric Theory of Dynamical Systems, Springer Verlag, New York, Heidelberg, and Berlin (1982).Google Scholar
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    D. K. Arrowsmith and C. M. Place, Ordinary Differential Equations. A Qualitative Approach with Applications, Chapman and Hall, London-New York (1982).Google Scholar
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    B. P. Demidovich, Lectures on Mathematical Stability Theory [in Russian], Nauka, Moscow (1967).Google Scholar
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    S. A. Vakhrameev and A. V. Sarychev, “The geometric control theory,” in: Progress in Science and Technology [in Russian], Ser. Algebra, Topology, Geometry, Vol. 23, Vses. Inst. Nauch. i Tekh. Inf., Moscow (1981), pp. 197–280.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • M. K. Sparavalo
    • 1
  1. 1.Military Aviation Engineering CollegeUSSR

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