Hybrid integral-differential-difference dynamic systems in symmetric form with memory loss
Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 113-125.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study linear nonstationary dynamical systems described by mixed integral-differential and integral-difference equations whose kernels are finite functions. For such systems, a generalized Cauchy formula is obtained for the integral representation of solutions based on the solutions of the corresponding adjoint systems. The results are refined in the stationary case.
@article{TIMB_2021_29_1_a10,
     author = {V. M. Marchenko},
     title = {Hybrid integral-differential-difference dynamic systems in symmetric form with memory loss},
     journal = {Trudy Instituta matematiki},
     pages = {113--125},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a10/}
}
TY  - JOUR
AU  - V. M. Marchenko
TI  - Hybrid integral-differential-difference dynamic systems in symmetric form with memory loss
JO  - Trudy Instituta matematiki
PY  - 2021
SP  - 113
EP  - 125
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a10/
LA  - ru
ID  - TIMB_2021_29_1_a10
ER  - 
%0 Journal Article
%A V. M. Marchenko
%T Hybrid integral-differential-difference dynamic systems in symmetric form with memory loss
%J Trudy Instituta matematiki
%D 2021
%P 113-125
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a10/
%G ru
%F TIMB_2021_29_1_a10
V. M. Marchenko. Hybrid integral-differential-difference dynamic systems in symmetric form with memory loss. Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 113-125. http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a10/

[1] Kirillova F.M., Streltsov S.V., “Neobkhodimye usloviya optimalnosti upravlenii v gibridnykh sistemakh”, Sb. trudov Instituta matematiki Sibirskogo otd. AN SSSR, Upravlyaemye sistemy, 14, Izd-vo Inst-ta matematiki SO AN SSSR, Novosibirsk, 1975, 24–33

[2] Akhundov A.A., “Upravlyaemost lineinykh gibridnykh sistem”, Sb. trudov Instituta matematiki Sibirskogo otd. AN SSSR, Upravlyaemye sistemy, 14, Izd-vo Inst-ta matematiki SO AN SSSR, Novosibirsk, 1975, 4–10

[3] Marchenko V.M., Poddubnaya O.N., “Predstavlenie reshenii upravlyaemykh gibridnykh sistem”, Problemy upravleniya i informatiki (Kiev), 2002, no. 6, 17–25

[4] Scheglova A.A., “Nablyudaemost vyrozhdennykh lineinykh gibridnykh sistem s postoyannymi koeffitsientami”, Avtomatika i telemekhanika, 2004, no. 11, 86–101

[5] De la Sen M., “The reachability and observability of hybrid multirate sampling linear systems”, Computers Math. Applic., 31:1 (1996), 109–122 | DOI | MR | Zbl

[6] Fridman E., “Stability of linear descriptor systems with delay: a Lyapunov-based approach”, J. Math. Anal. Appl., 273 (2002), 24–44 | DOI | MR | Zbl

[7] Marchenko V.M., Poddubnaya O.N., Zaczkiewicz Z., “On the observability of linear differential-algebraic systems with delays”, IEEE Trans. Automat. Control, 51:8 (2006), 1387–1392 | DOI | MR | Zbl

[8] Antsaklis P., Stiver J., Lemmon M., “Hybrid Systems Modeling and Autonomous Control Systems”, Lecture Notes in Computer Science, 736, Springer-Verlag, London, 1993, 366–392 | DOI

[9] Domek S., Kaszynski R. (Eds.), “Hybrid Systems: Computation and Control”, IEEE Sonf. MMAR'2004, v. 1, Control Theory, Control Engineering, Modelling and Simulation, 2004

[10] Kurzhanskii A. B., “Otchet o 16-m mezhdunarodnom kongresse IFAK (IFAC) – mezhdunarodnoi federatsii po avtomaticheskomu upravleniyu”, Avtomatika i telemekhanika, 2006, no. 1, 183–189

[11] Marchenko V.M., “DAD systems of control and observation and open problems”, International Journal: Mathematical Manuscripts (IJMM), 1:2 (2007), 111–125

[12] Marchenko V.M., “Vpolne regulyarnye sistemy s posledeistviem”, Tr. In-ta matematiki NAN Belarusi, 7 (2001), 97–104

[13] Marchenko V.M., “Gibridnye diskretno-nepreryvnye sistemy s upravleniem. I. Predstavlenie reshenii”, Differentsialnye uravneniya, 50:11 (2014), 1527–1540 | DOI | MR | Zbl

[14] Chistyakov V.F., Scheglova A.A., Izbrannye glavy teorii algebro-differentsialnykh sistem, Sibirskaya izdatelskaya firma RAN “Nauka”, Novosibirsk, 2003 | MR

[15] Asmykovich I.K., Deskriptornye sistemy upravleniya: bibliograficheskii ukazatel, BGTU, Minsk, 2020

[16] Marchenko V.M., “Upravlenie spektrom v gibridnykh differentsialno-raznostnykh sistemakh”, Differentsialnye uravneniya, 54:11 (2018), 1482–1496 | DOI | Zbl

[17] Marchenko V.M., Borkovskaya I.M., “O stabilizatsii skalyarnykh gibridnykh differentsialno-raznostnykh sistem”, Tr. BGTU. Ser. 3: Fiz.-mat. nauki i inform., 1(230), BGTU, Minsk, 2020, 5–13

[18] Myshkis A.D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR

[19] Bellman R., Kuk K.L., Differentsialno-raznostnye uravneniya, Mir, M., 1967

[20] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984

[21] Azbelev N.V., Maksimov V.P., Rakhmatullina L.F., Elementy sovremennoi teorii funktsionalno-differentsialnykh uravnenii. Metody i prilozheniya, Inst-t kompyutern. issledov., M., 2002 | MR

[22] Gabasov R., Kirillova F.M., Optimizatsiya lineinykh sistem, Izd-vo BGU, Minsk, 1973 | MR

[23] Moiseev N.N., Matematicheskie zadachi sistemnogo analiza, Nauka, M., 1981 | MR