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Automation and Remote Control

, Volume 62, Issue 9, pp 1428–1432 | Cite as

On Asymptotic Stability of the Rough Stationary Points of the Discontinuous Dynamic Systems on Plane

  • A. D. Myshkis
Article

Abstract

Consideration was given to the discontinuous (pulse) dynamic system on plane which obeys an ordinary autonomous system of differential equations of the first order and the law of skip xF(x) of the phase point occurring as soon as the point reaches the critical line M. It was assumed that the origin O was the stationary point of the original system of equations, the line M passed through O, F(O) = O, and the discontinuous system was structurally stable within some neighborhood of the point O. Under these assumptions, efficient necessary and sufficient conditions for asymptotic stability of the point O both relative to its full neighborhood and some sectors with centers at O were obtained.

Keywords

Differential Equation Dynamic System Mechanical Engineer System Theory Stationary Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • A. D. Myshkis
    • 1
  1. 1.Moscow State University of Railway TransportMoscowRussia

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