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On stability of controllable systems with descriptions containing only even derivatives

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Abstract

Consideration was given to stability of the controllable systems with descriptions containing only the even derivatives. An analytical method for calculation of the boundary of the stability domain on the plane of two parameters was proposed.

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References

  1. Rocard, Y., L’instabilité en mécanique; automobiles, avions, ponts suspendus, Paris: Masson, 1954. Translated under the title Neustoichivost’ v mekhanike, Moscow: Inostrannaya Literatura, 1959.

    Google Scholar 

  2. Strelkov, S.P., Vvedenie v teoriyu kolebanii (Introduction to the Oscillation Theory), Moscow: Nauka, 1964.

    Google Scholar 

  3. Ordanovich, A.E. and Rezaei Asl Abbas, Determination of the Stability Domains of the Controllable Mechanical Systems without Friction Forces and with Positional Feedback, Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., 2008, no. 4, pp. 66–68.

  4. Rezaei Asl Abbas and Ordanovich, A.E., Methods for Reduction of Combine’s Motional Oscillations, Cand. Sci. (Phys.-Math.) Dissertation, Moscow: Moscow State Univ., Inst. Mech., 2006.

    Google Scholar 

  5. Kirillov, O.N. and Seyranian, A.O., The Effect of Small Internal and External Damping on the Stability of Distributed Non-conservative Systems, J. Appl. Math. Mech., 2005, vol. 69(4), pp. 529–552.

    Article  MathSciNet  Google Scholar 

  6. Kirillov, O.N., Analysis of the Stability Domain Boundaries and Optimization of the Circulation Systems, Cand. Sci. Dissertation, Moscow: Moscow State Univ., 2000.

    Google Scholar 

  7. Bendrikov, G.A. and Teodorchik, K.F., Traektorii kornei lineinykh avtomaticheskikh sistem (Root Trajectories of the Linear Automatic Systems), Moscow: Nauka, 1964.

    Google Scholar 

  8. Vishnegradsky, I., Sur la théorie générale des régulateurs, Comptes Rendus, Acad., Sci. Paris, 1876, vol. 83, pp. 318–321.

    Google Scholar 

  9. Gryazina, E.N., Polyak, B.T., and Tremba, A.A., D-decomposition Technique State-of-the-Art, Autom. Remote Control, 2008, vol. 69, no. 12, pp. 1991–2026.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bulgakov, B.V., Discriminant Curve and the Domain of Aperiodic Stability, Dokl. Akad. Nauk SSSR, 1950, vol. LXXIII, no. 6, pp. 1143, 1144.

    Google Scholar 

  11. Bulgakov, B.V., Kolebaniya (Oscillations), Moscow: Gostekhizdat, 1954.

    Google Scholar 

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Original Russian Text © A.E. Ordanovich, 2012, published in Avtomatika i Telemekhanika, 2012, No. 5, pp. 14–24.

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Ordanovich, A.E. On stability of controllable systems with descriptions containing only even derivatives. Autom Remote Control 73, 778–785 (2012). https://doi.org/10.1134/S0005117912050025

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  • DOI: https://doi.org/10.1134/S0005117912050025

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