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Stabilization of the Motion of Pseudo-Linear Affine Systems

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Affine systems of special type are considered. For this class of system of equations, new conditions for stabilization of motion by a linear control of special type are established. These conditions are based on constraints for the fundamental matrix of linear approximation of the system and the vector function of nonlinearities. Both linear and nonlinear integral inequalities are used

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References

  1. G. Ascoli, “Osservazioni sopra alcune questioni di stabilita 1,” Atti Acccad. Naz. Lincei Rend. Cl.Sci. Fis. Mat. Nat., No. 9, 129–134 (1950).

  2. E. A. Babenko and A. A. Martynyuk, “Stabilization of the motion of a nonlinear system with interval initial conditions,” Int. Appl. Mech., 52, No. 2, 182–191 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. E. A. Babenko and A. A. Martynyuk, “Effectiveness of a roller damper in suppressing conductor galloping,” Int. Appl. Mech., 52, No. 4, 413–421 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Bacciotti and F. Ceragioli, Stability and Stabilization of Discontinuous Systems and Non smooth Lyapunov Functions, Dip. di Mat. del Politecnico di Torino, Manuscript (2016).

  5. F. J. Christophersen, Optimal Control and Analysis for Constrained Piecewise Affine Systems, Diss. ETH, Zurich, No. 16807, Manuscript (2006).

  6. A. Elakkary and N. Elalami, “Stabilizability: Application for attitude control systems of micro satellite,” J. Theor. Appl. Inform. Technol., 5, 325–333 (2014).

    Google Scholar 

  7. Y. Louartassi, Elhoussine El Mazoudi, and N. Elalami, “A new generalization of lemma Gronwall–Bellman,” Appl. Math. Sci., 6, No. 13, 621–628 (2012).

  8. A. A. Martynyuk, “Novel bounds for solutions of nonlinear differential equations,” Appl. Math., No. 6, 182–194 (2015).

  9. A. A. Martynyuk and E. A. Babenko, “Finite time stability of uncertain affine systems,” Math. Eng. Sci. Aerospace, 7, No. 1, 179–196 (2016).

    Google Scholar 

  10. A. A. Martynyuk, D. Ya. Khusainov, and V. A. Chernienko, “Integral estimates of solution to nonlinear systems and their applications,” Nonlin. Dynam. Syst. Theory, 16, No. 1, 1–11 (2016).

  11. M. Rama Mohana Rao, Ordinary Differential Equations: Theory and Applications, Affiliated East-West Press Pvt Ltd, New Delhi-Madras (1980).

  12. A. Skullestad and J. Gilbert, “H control of gravity gradient stabilized satellite,” Contr. Eng. Pract., 8, 975–983 (2000).

    Article  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    A. A. Martynyuk, L. N. Chernetskaya & Yu. A. Martynyuk-Chernienko

Authors
  1. A. A. Martynyuk
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  2. L. N. Chernetskaya
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  3. Yu. A. Martynyuk-Chernienko
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Correspondence to A. A. Martynyuk.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 53, No. 3, pp. 113–120, May–June, 2017.

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Martynyuk, A.A., Chernetskaya, L.N. & Martynyuk-Chernienko, Y.A. Stabilization of the Motion of Pseudo-Linear Affine Systems. Int Appl Mech 53, 334–341 (2017). https://doi.org/10.1007/s10778-017-0815-5

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  • DOI: https://doi.org/10.1007/s10778-017-0815-5

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