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Exponential stability of motion determined by two measures

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Abstract

The conditions of exponential (ρ{su0},ρ{su1}) of a system of differential equations modeling the motion of a system with a finite number of degrees of freedom are determined with respect to two measures. The main result is applied to a problem concerning the exponential stoppage of a mechanical system.

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References

  1. V. Lakshmikantham, S. Liila, and A. A. Martynyuk,Stability of Motion. Comparison Method [in Russian], Nauk. Dumka, Kiev (1991).

    Google Scholar 

  2. A. M. Lyapunov, “Study of a special case of the problem of the stability of motion,”Mat. Sb.,XVII, No. 2, 253–333 (1893).

    Google Scholar 

  3. A. A. Martynyuk, and A. N. Chenienko, “Stability of motion based on two measures,”Dopov. Nats. Akad. Nauk Ukrainy, No. 2, 44–48 (1998).

    Google Scholar 

  4. A. A. Martynyuk, and A. N. Chernienko, “Uniform stability of motion according to two measures,”Dopov. Nats. Akad. Nauk Ukrainy, No. 3, 14–17 (1998).

    Google Scholar 

  5. A. A. Martynyuk, “Exponential polystability of branching motions,”Ukr. Mat. Zh.,48, No. 5, 642–649 (1996).

    Google Scholar 

  6. I. Tereki, and L. Khatvani, “Asymptotic stoppage in the presence of dry friction,”Prikl. Mat. Mekh.,46, No. 1, 20–26 (1982).

    Google Scholar 

  7. V. Lakshmikantham and L. Salvadori, “On Massera type converse theorem in terms of two different measures”,Bull. U.M.I.,13, 293–301 (1976).

    MATH  Google Scholar 

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Additional information

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 103–107, March, 1999.

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Chernienko, A.N. Exponential stability of motion determined by two measures. Int Appl Mech 35, 315–320 (1999). https://doi.org/10.1007/BF02682130

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  • DOI: https://doi.org/10.1007/BF02682130

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