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On sufficient conditions for the technical stability of controlled processes with lumped parameters

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Abstract

On the basis of the theory of differential inequalities and Lagrange multipliers, we develop a method for the investigation of conditions for the technical stability of continuously controlled processes with lumped parameters.

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References

  1. K. A. Abgaryan, “Stability of motion on a finite time interval,” in: VINITI Series in General Mechanics [in Russian], Vol. 3, VINITI, Moscow (1976), pp. 43–127.

    Google Scholar 

  2. R. Z. Abdullin, “Practical stability in problems of automatic control,” in: Dynamics of Nonlinear Systems [in Russian], Nauka, Novosibirsk (1983), pp. 35–49.

    Google Scholar 

  3. F. D. Bairamov, “Provision of technical stability of controlled systems,” in: Problems of Analytical Mechanics, Stability, and Motion Control [in Russian], Nauka, Novosibirsk (1991), pp. 134–139.

    Google Scholar 

  4. V. I. Vasyukov and S. A. Gorbatenko, “Construction of a control law for a nonlinear system on the basis of the solution of the inverse problem of dynamics,” in: Problems of Analytical Mechanics, Stability, and Motion Control [in Russian], Nauka, Novosibirsk (1991), pp. 140–144.

    Google Scholar 

  5. F. G. Gerashchenko and N. F. Kirichenko, “Investigation of problems of practical stability and stabilization of motion,” Mekh. Tverd. Tela, No. 6, 15–24 (1975).

  6. V. I. Zubov, Dynamics of Controlled Systems [in Russian], Vysshaya Shkola, Moscow (1982).

    MATH  Google Scholar 

  7. G. V. Kamenkov, “On stability on a finite time interval,” Prikl. Mat. Mekh., 25, Issue 5, 529–540 (1953).

    MathSciNet  Google Scholar 

  8. N. F. Kirichenko, Introduction to the Theory of Stabilization of Motion [in Russian], Vyshcha Shkola, Kiev (1978).

    Google Scholar 

  9. N. A. Kil’chevskii, A Course in Theoretical Mechanics [in Russian], Vol. 1, Nauka, Moscow (1977).

    Google Scholar 

  10. A. M. Letov, Mathematical Theory of Control Processes [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  11. T. K. Sirazetdinov, “Optimization of controlled processes,” Izv. Vyssh. Uchebn. Zaved., Ser. Aviats. Tekh., No. 4, 96–102 (1974).

  12. V. M. Kuntsevich and M. M. Lychak, Synthesis of Systems of Automatic Control with the Use of the Lyapunov Functions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  13. K. S. Matviichuk, “On the technical stability of dynamical states of a solid body oscillating on nonlinear elastic shock-absorbers,” Prikl. Mekh., 29, No. 7, 90–96 (1993).

    MathSciNet  Google Scholar 

  14. K. S. Matviichuk, “Technical stability of the process of motion of two connected platforms carrying moving flywheels,” Izv. RAN, Ser. Mekh. Tverd. Tela, No. 6, 3–10 (1993).

  15. K. S. Matviichuk, “On the technical stability of a system of automatic control with variable structure,” Prikl. Mekh., 30, No. 10, 74–78 (1994).

    MathSciNet  Google Scholar 

  16. J. Szarski, Differential Inequalities, PWN, Warsaw (1967).

    MATH  Google Scholar 

  17. B. Skalmierski and A. Tylikowski, Stabilnosc Ukladow Dynamicznych, PWN, Warsaw (1967).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, Ukrainian Academy of Sciences, Kiev

    K. S. Matviichuk

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  1. K. S. Matviichuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1352–1358, October, 1998.

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Matviichuk, K.S. On sufficient conditions for the technical stability of controlled processes with lumped parameters. Ukr Math J 50, 1544–1550 (1998). https://doi.org/10.1007/BF02513502

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  • DOI: https://doi.org/10.1007/BF02513502

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