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Stabilization of a system with a constant and a linear delay

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REFERENCES

  1. Bellman, R. and Cooke, K., Differential-Difference Equations, New York, 1963. Translated under the title Differentsial’no-raznostnye uravneniya, Moscow: Mir, 1967.

  2. El’sgol’ts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial’nykh uravnenii s otklonyayushchimsya argumentom (Introduction to the Theory of Differential Equations with a Deviating Argument), Moscow, 1971.

  3. Ockendon, J. and Taylor, A., Proc. Roy. Soc. London. Ser A., 1971, vol. 322, pp. 447–468.

    Google Scholar 

  4. Grebenshchikov, B.G., Izv. RAN. Teoriya i Sistemy Upravleniya, 2001, no. 5, pp. 5–15.

  5. Markvardt, N.G. and Vlasov, I.I., Kontaktnaya set’ (Aerial Contact Wire), Moscow, 1978.

  6. Grebenshchikov, B.G. and Rozhkov, V.I., Differents. Uravn., 1993, vol. 29, no. 5, pp. 751–758.

    Google Scholar 

  7. Markushin, E.M., Optimal’nye sistemy avtomaticheskogo regulirovaniya s zapazdyvaniem po vremeni (Optimal Systems of Automated Regulation with Time Delay), Saratov, 1971.

  8. Osipov, Yu.S., Differents. Uravn., 1965, vol. 1, no. 5, pp. 605–618.

    Google Scholar 

  9. Shimanov, S.N., Ustoichivost’ lineinykh sistem s periodicheskimi koeffitsientami i s zapazdyvaniem (Stability of Linear Systems with Periodic Coefficients and with Delay), Sverdlovsk, 1983.

  10. Grebenshchikov, B.G., O stabilizatsii statsionarnykh lineinykh sistem s zapazdyvaniem, lineino zavisyashchim ot vremeni (On Stabilization of Stationary Linear Systems with Delay Linearly Depending on Time), Deposited in VINITI, Moscow, 1982, no. 4384–V92.

  11. Furasov, V.D., Ustoichivost’ dvizheniya, otsenki i stabilizatsiya (Stability of Motion, Estimates, and Stabilization), Moscow, 1977.

  12. Kim, A.V., Kwon, W.H., Pimenov, V.G., et al., Time-Delay System Toolbox (for Use with MATLAB). Beta Version, Korea, Seoul, 1998.

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Translated from Differentsial’nye Uravneniya, Vol. 40, No. 12, 2004, pp. 1587–1595.

Original Russian Text Copyright © 2004 by Grebenshchikov, Lozhnikov.

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Grebenshchikov, B.G., Lozhnikov, A.B. Stabilization of a system with a constant and a linear delay. Diff Equat 40, 1667–1675 (2004). https://doi.org/10.1007/s10625-005-0098-1

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  • DOI: https://doi.org/10.1007/s10625-005-0098-1

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