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Realization of dynamical systems in scales of systems with aftereffect: I. Realizability

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References

  1. Gilbert, E.G., SIAM J. Control, 1963, no. 1, pp. 128–151.

  2. Kalman, R.E., SIAM J. Control, 1963, no. 1, pp. 152–192.

  3. Kalman, R., Falb, P., and Arbib, M., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971.

    MATH  Google Scholar 

  4. Kamen, E.W., Lectures on Algebraic System Theory: Linear Systems over Rings, NASA Contractor Report, 1978, no. 3016.

  5. Kamen, E.W., J. Differ. Equat., 1978, vol. 27, pp. 274–297.

    Article  MathSciNet  Google Scholar 

  6. Rouchaleau, Y., Linear, Discrete-Time, Time-Dimensional Dynamical Systems over Some Classes of Commutative Rings, Ph. D. Dissertation, Stanford University, 1972.

  7. Rouchaleau, Y., Wyman, B.F., and Kalman, R.E., Proc. Natl. Acad. Sci. USA, 1972, vol. 69, pp. 3404–3406.

    Article  MathSciNet  MATH  Google Scholar 

  8. Sontag, E.D., Richerche di Automatica, 1976, vol. 7, no. 1, pp. 1–34.

    Google Scholar 

  9. Eising, R. and Hautus, M.L.J., Math. Systems Theory, 1981, no. 14, pp. 353–366.

  10. Eising, R., IEEE Trans. Automat. Control, 1978, vol. AC-23, no. 5, pp. 793–799.

    Article  MathSciNet  Google Scholar 

  11. Kung, S.Y., Levy, B., Morf, M., and Kailath, T., Proc. IEEE, 1977, vol. 65, pp. 945–961.

    Article  Google Scholar 

  12. Loiseau, J.-J., Proc. CESA’96, Lille, 1996, pp. 97–100.

  13. Zak, S.N., Lee, E.B., and Lu, W.S., IEEE Trans. Circuits Systems, 1986. CAS-33, no. 12, pp. 1241–1244.

  14. Morse, A.S., Automatica J. IFAC, 1976, vol. 12, pp. 529–531.

    Article  MathSciNet  MATH  Google Scholar 

  15. Cliff, E.M. and Burns, J.A., Math. Systems Theory, 1978, vol. 12, pp. 133–149.

    Article  MathSciNet  MATH  Google Scholar 

  16. Luazo, J.-J. and Marchenko, V.M., Dokl. Akad. Nauk, 2002, vol. 383, no. 3, pp. 305–308.

    MathSciNet  Google Scholar 

  17. Marchenko, V.M., Tez. dokl. V Resp. mat. konf. (Abstr. V Republ. Math. Conf.), Grodno, 1980, part 1, p. 156.

  18. Pandolfi, L., SIAM J. Control Optim., 1983, vol. 21, pp. 598–613.

    Article  MathSciNet  MATH  Google Scholar 

  19. Mathematical System Theory: The Influence of R.E. Kalman, Antoulas, A.C., Ed., Berlin, 1991.

  20. Gabasov, R., Kirillova, F.M., Marchenko, V.M., and Asmykovich, I.K., Control and Observation Problems for Infinite-Dimensional Systems, Preprint Inst. Math. Acad. Sci. Belarus, Minsk, 1984, no. 1(186).

  21. Marchenko, V.M., Vestn. Beloruss. Gos. Univ. Ser. 1. Fiz. Mat. Inform., 1972, no. 3, pp. 11–13.

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Original Russian Text © V.M. Marchenko, J.-J. Loiseau, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1515–1523.

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Marchenko, V.M., Loiseau, J.J. Realization of dynamical systems in scales of systems with aftereffect: I. Realizability. Diff Equat 42, 1587–1595 (2006). https://doi.org/10.1134/S0012266106110085

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  • DOI: https://doi.org/10.1134/S0012266106110085

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