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System Embedding. Polynomial Equations

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Abstract

The class of solutions of the polynomial equations including their generalizations in the form of the Bézout matrix identities was constructed analytically using the technology of constructive system embedding. The structure of a solution depends on the number of steps of the Euclidean algorithm and is obtained explicitly by appropriate substitutions. Illustrative and descriptive examples are presented.

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REFERENCES

  1. Volgin, L.N., Optimal'noe diskretnoe upravlenie dinamicheskimi sistemami (Optimal Discrete Control of Dynamic Systems), Moscow: Nauka, 1986.

    Google Scholar 

  2. Tsypkin, Ya.Z. and Vishnyakov, A.N., Design of Modal Discrete Control Systems, Avtom.Telemekh., 1993, no. 7, pp. 86–94.

  3. Polyak, B.T., New Approaches to Control of the Discrete Systems under Bounded Perturbations, Mezhdunar.konf.po problemam upravleniya.Sb.plenarnyh dokl. (Int. Conf. on Problems of Control. Plenary Papers), Moscow: Inst. Probl. Upravlen., 1999, pp. 111–117.

    Google Scholar 

  4. Rozenvasser, E.N., Design of Multidimensional Linear Systems with Given Characteristic Polynomial, Avtom.Telemekh., 1996, no. 8, pp. 35–55.

  5. Kailath, T., Linear Systems, Englewood Cliffs: Prentice Hall, 1980.

    Google Scholar 

  6. Youla, D.C., Jabr, H.A., and Bongiorno, J.J., Modern Wiener-Hopf Design of Optimal Controllers. Pt. 2. Multivariable Case, IEEE Trans.Autom.Control, 1976, vol. 21, no. 3, pp. 319–338.

    Google Scholar 

  7. Vinogradov, I.M., Osnovy teorii chisel (Fundamentals of the Number Theory), Moscow: Nauka, 1985.

    Google Scholar 

  8. van der Waerden, B.L., Algebra I., Berlin: Springer, 1971, Algebra II., Berlin: Springer, 1967. Translated under the title Algebra, Moscow: Nauka, 1976.

    Google Scholar 

  9. Cohn, P.M., Free Rings and Their Relations, London: Academic, 1971. Translated under the title Svobodnye kol'tsa i ikh svyazi, Moscow: Mir, 1975.

    Google Scholar 

  10. Bukov, V.N. and Ryabchenko, V.N., System Embedding. Promatrices, Avtom.Telemekh., 2000, no. 4, pp. 20–33.

  11. Bukov, V.N. and Ryabchenko, V.N., System Embedding. Arbitrary Transforms, Avtom.Telemekh., 2000, no. 12, pp. 3–14.

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  1. Military Aviation Technical University, Moscow, Russia

    V. N. Bukov, V. V. Kos'yanchuk & V. N. Ryabchenko

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  1. V. N. Bukov
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  2. V. V. Kos'yanchuk
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  3. V. N. Ryabchenko
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Bukov, V.N., Kos'yanchuk, V.V. & Ryabchenko, V.N. System Embedding. Polynomial Equations. Automation and Remote Control 63, 1051–1061 (2002). https://doi.org/10.1023/A:1016198529243

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