@article{TIMM_2013_19_1_a17,
author = {N. Yu. Lukoyanov and A. R. Plaksin},
title = {Finite-dimensional modeling guides in time-delay systems},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {182--195},
year = {2013},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a17/}
}
N. Yu. Lukoyanov; A. R. Plaksin. Finite-dimensional modeling guides in time-delay systems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 182-195. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a17/
[1] Krasovskii N. N., Nekotorye zadachi teorii ustoichivosti dvizheniya, Fizmatgiz, M., 1959, 211 pp. | MR
[2] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972, 352 pp. | MR | Zbl
[3] Bellman R., Kuk K. L., Differentsialno-raznostnye uravneniya, Mir, M., 1967, 548 pp. | MR | Zbl
[4] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984, 421 pp. | MR
[5] Myshkis A. D., Shimanov S. N., Elsgolts L. E., “Kolebaniya i ustoichivost sistem s zapazdyvaniem”, Tr. Mezhdunar. simpoziuma po nelineinym kolebaniyam, v. 2, Kiev, 1963, 241–267
[6] Shimanov S. N., “K teorii lineinykh differentsialnykh uravnenii s posledeistviem”, Differents. uravneniya, 1:1 (1965), 102–116 | Zbl
[7] Shimanov S. N., Ustoichivost lineinykh sistem s periodicheskimi koeffitsientami i zapazdyvaniem, Izd-vo Uralskogo universiteta, Sverdlovsk, 1983, 64 pp. | MR
[8] Dolgii Yu. F., Shimanov S. N., K approksimatsii lineinykh differentsialnykh uravnenii s zapazdyvaniem, Dep. v VINITI 27.05.1977, No 2078-77, UrGU, Sverdlovsk, 1977, 17 pp.
[9] Krasovskii N. N., “Ob approksimatsii odnoi zadachi analiticheskogo konstruirovaniya regulyatorov v sisteme s zapazdyvaniem”, Prikl. matematika i mekhanika, 28:4 (1964), 716–724 | MR
[10] Krasovskii N. N., “Ob approksimatsii odnoi zadachi ob optimalnom upravlenii v sisteme s posledeistviem”, Dokl. AN SSSR, 167:3 (1966), 540–542 | MR
[11] Repin Yu. M., “O priblizhennoi zamene sistem s zapazdyvaniem obyknovennymi dinamicheskimi sistemami”, Prikl. matematika i mekhanika, 29:2 (1965), 226–235 | MR | Zbl
[12] Salukvadtse M. E., “K zadache sinteza optimalnogo regulyatora v lineinykh sistemakh s zapazdyvaniem, podverzhennykh postoyanno deistvuyuschim vozmuscheniyam”, Avtomatika i telemekhanika, 23:2 (1962), 1595–1601
[13] Kurzhanskii A. B., “K approksimatsii lineinykh differentsialnykh uravnenii s zapazdyvaniem”, Differents. uravneniya, 3:12 (1967), 2094–2107
[14] Banks H. T., Burns J. A., “Hereditary control problems: Numerical methods based on averaging approximations”, SIAM J. Control Optim., 16 (1978), 169–208 | DOI | MR | Zbl
[15] Banks H. T., Kappel F., “Spline approximations for functional differential equations”, J. Different. Equat., 34:3 (1979), 496522 | DOI | MR
[16] Kryazhimskii A. V., Maksimov V. I., “Approksimatsiya lineinykh differentsialno-raznostnykh igr”, Prikl. matematika i mekhanika, 42:2 (1978), 202–209 | MR
[17] Maksimov V. I., “Approksimatsiya nelineinykh differentsialno-raznostnykh igr”, Optim. upr. v dinam. sistemakh, Sb. st., Tr. In-ta matematiki i mekhaniki UNTs AN SSSR, 30, Sverdlovsk, 1979, 49–65 | MR | Zbl
[18] Oparin N. P., “Ob approksimatsii sistem neitralnogo tipa”, Differents. uravneniya s otklonyayuschimisya argumentami, Sb. nauch. tr., 11, Un-t Druzhby narodov im. P. Lumumby, M., 1979, 52–60 | MR
[19] Kunisch K., “Approximation Schemes for Nonlinear Neutral Optimal Control Systems”, J. Math. Anal. Appl., 82 (1980), 112–143 | DOI | MR
[20] Dolgii Yu. F., Sazhina S. D., “Otsenka eksponentsialnoi ustoichivosti sistem s zapazdyvaniem metodom approksimiruyuschikh sistem”, Differents. uravneniya, 21:12 (1985), 2046–2052 | MR
[21] Krasovskii N. N., Kotelnikova A. N., “Stokhasticheskii povodyr dlya ob'ekta s posledeistviem v pozitsionnoi differentsialnoi igre”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 2, 2011, 97–104
[22] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 458 pp. | MR | Zbl
[23] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 516 pp. | MR
[24] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972, 496 pp. | MR
[25] DeVore R. A., Lorentz G. G., Constructive approximation, Springer-Verlag, Berlin, 1993, 449 pp. | MR