Automation and Remote Control

, Volume 62, Issue 9, pp 1534–1542 | Cite as

On the Right Solutions of a Class of Discontinuous Systems. I

  • I. A. Finogenko


A method for specifying the differential equations with a discontinuous right-hand side was proposed. It allows one to describe all kinds of the right motions of some classes of controllable discontinuous systems. The method is implicit and relies on the necessary existence conditions for the right solutions of equations in the contingencies obtained from the original system.


Differential Equation Mechanical Engineer System Theory Original System Existence Condition 
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  1. 1.
    Aizerman, M.A. and Pyatnitskii, E.S., Fundamentals of the Theory of Discontinuous Systems. I, II, Avtom. Telemekh., 1974, no. 7, pp. 33-47; no. 8, pp. 39-61.Google Scholar
  2. 2.
    Filippov, A.F., Differentsial'nye uravneniya s razryvnoi pravoi chast'yu (Differential Equations with Discontinuous Right-hand Side), Moscow: Nauka, 1985.Google Scholar
  3. 3.
    Matrosov, V.M., On Differential Equations and Inequalities with Discontinuous Right-hand Sides. I, II, Diff. Uravn., 1967, vol. 3, no. 3, pp. 395-409; no. 5, pp. 839-848.Google Scholar
  4. 4.
    Tolstonogov, A.A., Differentsial'nye vklyucheniya v banakhovom prostranstve (Differential Inclusions in the Banach Space), Novosibirsk: Nauka, 1986.Google Scholar
  5. 5.
    Utkin, V. I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.Google Scholar
  6. 6.
    Filippov, A.F., On some Issues of the Optimal Control Theory, Vestn. MGU, 1959, no. 2, pp. 25-32.Google Scholar
  7. 7.
    Pyatnitskii, E.S., Decomposition-based Design of the Hierarchical Control Systems of Mechanical and Electromechanical Plants I, II, Avtom. Telemekh., 1989, no. 1, pp. 87-98; no. 2, pp. 57-70.Google Scholar
  8. 8.
    Matyukhin, V.I., Stability of the Manifolds of the Manipulator Controllable Motions, Avtom. Telemekh., 1998, no. 4, pp. 47-56.Google Scholar
  9. 9.
    Matyukhin, V.I., Motional Stability of the Manipulation Robots in the Decomposition State, Avtom. Telemekh., 1989, no. 3, pp. 33-44.Google Scholar
  10. 10.
    Matrosov, V.M. and Finogenko, I.A., On Solvability of the Motion Equation of Mechanical Systems with Gliding Friction, Prikl. Mat. Mekh., 1994, vol. 58, no. 6, pp. 3-13.Google Scholar
  11. 11.
    Lur'e, A.I., Analiticheskaya mekhanika (Analytical Mechanics), Moscow: Fizmatgiz, 1961.Google Scholar
  12. 12.
    Appel', P., Teoreticheskaya mekhanika (Theoretical Mechanics), Moscow: Fizmatgiz, 1960, vol. 2.Google Scholar
  13. 13.
    Kantorovich, L.V. and Akilov, G.P., Funktsional'nyi analiz (Functional Analysis), Moscow: Nauka, 1977.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • I. A. Finogenko
    • 1
  1. 1.Institute of System Dynamics and Control Theory, Siberian BranchRussian Academy of SciencesIrkutskRussia

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