Geodesic
Damping problem for control system with delay with different number of inputs and outputs
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 189-200.

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

We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coefficients and several delays. A connection has been established between the variational problem corresponding to the problem of calming a system with delay and the boundary value problem for a system of second-order differential equations. A priori estimates of solutions are obtained. A theorem on the solvability of the considered boundary value problem is proved.
Keywords: differential-difference equation of neutral type, control system with delay, damping problem, variational problem. 
@article{CMFD_2024_70_2_a0,
     author = {A. Sh. Adkhamova and A. L. Skubachevskii},
     title = {Damping problem for control system with delay with different number of inputs and outputs},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {189--200},
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a0/}
}
TY  - JOUR
AU  - A. Sh. Adkhamova
AU  - A. L. Skubachevskii
TI  - Damping problem for control system with delay with different number of inputs and outputs
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2024
SP  - 189
EP  - 200
VL  - 70
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a0/
LA  - ru
ID  - CMFD_2024_70_2_a0
ER  - 
%0 Journal Article
%A A. Sh. Adkhamova
%A A. L. Skubachevskii
%T Damping problem for control system with delay with different number of inputs and outputs
%J Contemporary Mathematics. Fundamental Directions
%D 2024
%P 189-200
%V 70
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a0/
%G ru
%F CMFD_2024_70_2_a0
A. Sh. Adkhamova; A. L. Skubachevskii. Damping problem for control system with delay with different number of inputs and outputs. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 189-200. http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a0/

[1] Adkhamova A. Sh., “Gladkost reshenii zadachi ob uspokoenii nestatsionarnoi sistemy upravleniya s posledeistviem”, Sovrem. mat. Fundam. napravl., 68, no. 1, 2022, 14–24

[2] Adkhamova A. Sh., “Gladkost reshenii zadachi ob uspokoenii nestatsionarnoi sistemy upravleniya s posledeistviem neitralnogo tipa na vsem intervale”, Sovrem. mat. Fundam. napravl., 69, no. 1, 2023, 1–17 | MR

[3] Adkhamova A. Sh., Skubachevskii A. L., “Ob odnoi zadache uspokoeniya nestatsionarnoi sistemy upravleniya s posledeistviem”, Sovrem. mat. Fundam. napravl., 65, no. 4, 2019, 547–556

[4] Adkhamova A. Sh., Skubachevskii A. L., “Ob uspokoenii sistemy upravleniya s posledeistviem neitralnogo tipa”, Dokl. RAN, 490:1 (2020), 81–84 | DOI | MR | Zbl

[5] Adkhamova A. Sh., Skubachevskii A. L., “Ob odnoi kraevoi zadache dlya sistemy differentsialno-raznostnykh uravnenii zapazdyvayuschego tipa”, Diff. uravnyu, 58:6 (2022), 747–755 | MR | Zbl

[6] Danford N., Shvarts Dzh., Lineinye operatory, v. 2, Spektralnaya teoriya, Mir, M., 1966

[7] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968

[8] Kryazhimskii A. V., Maksimov V. I., Osipov Yu. S., “O pozitsionnom modelirovanii v dinamicheskikh sistemakh”, Prikl. mat. mekh., 47:6 (1983), 883–890 | MR

[9] Leonov D. D., “K zadache ob uspokoenii sistemy upravleniya s posledeistviem”, Sovrem. mat. Fundam. napravl., 37, 2010, 28–37

[10] Osipov Yu. S., “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Diff. uravn., 1:5 (1965), 605–618 | Zbl

[11] Skubachevskii A. L., “K zadache ob uspokoenii sistemy upravleniya s posledeistviem”, Dokl. RAN, 335:2 (1994), 157–160 | Zbl

[12] Adkhamova A. S., Skubachevskii A. L., “Damping problem for multidimensional control system with delays”, Distrib. Comput. Commun. Networks, 678 (2016), 612–623 | DOI | Zbl

[13] Banks H. T., Kent G. A., “Control of functional differential equations of retarded and neutral type to target sets in function space”, SIAM J. Control, 10:4 (1972), 567–593 | DOI | MR | Zbl

[14] Kent G. A., “A maximum principle for optimal control problems with neutral functional differential systems”, Bull. Am. Math. Soc., 77:4 (1971), 565–570 | DOI | MR | Zbl

[15] Skubachevskii A. L., Elliptic functional differential equations and applications, Birkhäuser, Basel—Boston—Berlin, 1997 | MR | Zbl