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Popova, Svetlana Nikolaevna

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Total publications: 34
Scientific articles: 28

Number of views:
This page:1997
Abstract pages:4479
Full texts:1809
References:459
Associate professor
Doctor of physico-mathematical sciences (2005)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 14.12.1965
Phone: +7 (3412) 91 60 92
Fax: +7 (3412) 75 58 66
E-mail:
Keywords: ordinary differential equations, Lyapunov exponents, lyapunov invariants, linear closed-loop control, stabilization, controllability, observability.
UDC: 517.926, 517.977
MSC: 34d08, 34d20, 34d23, 49n35, 93b05, 93b07, 93b52, 93C05, 34H15, 93D15

Subject:

Problems of controllability by various totalities of Lyapunov invariants of linear differential systems in the form of $\dot x=A(t)x+B(t)u$, $x\in\mathbb R^n$, $u\in\mathbb R^m$ under the action linear closed-loop control $u=U(t)x$ are investigated. A concept of local controllability by Lyapunov exponents was proposed; sufficient conditions of this controllability were obtained. It was proved (with E. K. Makarov) a global controllability by full totality of Lyapunov invariants of two-dimensional linear systems under the condition of uniform complete controllability of the pair $(A,B)$. In the papers with E. L. Tonkov a concept of uniform consistency of linear control systems with observer was proposed; an applicability of V. M. Millionshchikov rotation method to such systems was proved.

Biography

Graduated from Faculty of Mathematics of Udmurt State University (UdSU) in 1988. Ph.D. thesis was defended in 1992. D.Sci. thesis was defended in 2005. List of my works contains more than 40 titles. Now I am a professor of the department of differential equations in UdSU.

   
Main publications:
  1. Makarov E.K., Popova S.N., Upravlyaemost asimptoticheskikh invariantov nestatsionarnykh lineinykh sistem, Belorusskaya nauka, Minsk, 2012
  2. Popova S.N., “O globalnoi upravlyaemosti pokazatelei Lyapunova lineinykh sistem”, Differentsialnye uravneniya, 43:8 (2007), 1048-1054

http://www.mathnet.ru/eng/person18005
List of publications on Google Scholar
List of publications on ZentralBlatt
http://elibrary.ru/author_items.asp?spin=4800-5518
http://orcid.org/0000-0001-5501-474X
http://www.researcherid.com/rid/E-8968-2014
http://www.scopus.com/authid/detail.url?authorId=7101950545

Publications in Math-Net.Ru
2019
1. E. K. Makarov, S. N. Popova, “On the definition of uniform complete observability”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019),  129–140  mathnet  elib
2. I. N. Banshchikova, E. K. Makarov, S. N. Popova, “On the conditions of proportional local assignability of the Lyapunov spectrum of a linear discrete-time system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:3 (2019),  301–311  mathnet
2017
3. S. N. Popova, I. N. Banshchikova, “Spectral set of a linear system with discrete time”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  101–104  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 230:5 (2018), 752–756  scopus
4. I. N. Banshchikova, S. N. Popova, “On the property of integral separation of discrete-time systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017),  481–498  mathnet  elib
5. E. K. Makarov, S. N. Popova, “On the definition of uniform complete controllability”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017),  326–343  mathnet  elib
2016
6. I. N. Banshchikova, S. N. Popova, “On the spectral set of a linear discrete system with stable Lyapunov exponents”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  15–26  mathnet  mathscinet  elib
2014
7. V. A. Zaitsev, S. N. Popova, E. L. Tonkov, “On the property of uniform complete controllability of a discrete-time linear control system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 4,  53–63  mathnet
2013
8. I. N. Banshchikova, S. N. Popova, “On the property of the closedness of the set of almost periodic functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, 4,  13–19  mathnet
2012
9. I. S. Zagrebina, S. N. Popova, “On Lyapunov exponents of the simplest time-lag equation”, Izv. IMI UdGU, 2012, 1(39),  54  mathnet  elib
2010
10. V. A. Zaitsev, S. N. Popova, E. L. Tonkov, “Exponential stabilization of nonlinear control systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, 3,  25–29  mathnet
11. S. N. Popova, “Sufficient conditions of global attainability of linear control system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, 1,  73–80  mathnet
2008
12. S. N. Popova, “Control over asymptotic invariants for the systems with almost periodic coefficients”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, 2,  117–118  mathnet
2006
13. V. A. Zaitsev, E. K. Makarov, S. N. Popova, E. L. Tonkov, “Problems of control over Lyapunov invariants”, Izv. IMI UdGU, 2006, 3(37),  43–48  mathnet
2004
14. S. N. Popova, “Simultaneous Local Controllability of the Spectrum and the Lyapunov Irregularity Coefficient of Regular Systems”, Differ. Uravn., 40:3 (2004),  425–428  mathnet  mathscinet; Differ. Equ., 40:3 (2004), 461–465
15. S. N. Popova, “Global Reducibility of Linear Control Systems to Systems of Scalar Type”, Differ. Uravn., 40:1 (2004),  41–46  mathnet  mathscinet; Differ. Equ., 40:1 (2004), 43–49
2003
16. S. N. Popova, “Global Controllability of the Complete Set of Lyapunov Invariants of Periodic Systems”, Differ. Uravn., 39:12 (2003),  1627–1636  mathnet  mathscinet; Differ. Equ., 39:12 (2003), 1713–1723
17. E. K. Makarov, S. N. Popova, “Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems”, Differ. Uravn., 39:2 (2003),  217–226  mathnet  mathscinet; Differ. Equ., 39:2 (2003), 234–245
18. S. N. Popova, “Local Attainability for Linear Control Systems”, Differ. Uravn., 39:1 (2003),  50–56  mathnet  mathscinet; Differ. Equ., 39:1 (2003), 51–58
2002
19. S. N. Popova, “On global controllability of the complete set of Lyapunov invariants for periodic systems”, Izv. IMI UdGU, 2002, 2(25),  79–80  mathnet
20. S. N. Popova, “On the equivalence of local admissibility and complete controllability of linear systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, 6,  50–53  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 46:6 (2002), 48–51
1999
21. E. K. Makarov, S. N. Popova, “On the global controllability of a complete set of Lyapunov invariants of two-dimensional linear systems”, Differ. Uravn., 35:1 (1999),  97–106  mathnet  mathscinet; Differ. Equ., 35:1 (1999), 97–107
22. E. K. Makarov, S. N. Popova, “On the global controllability of central exponents of linear systems.”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, 2,  60–67  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 43:2 (1999), 56–63
1997
23. E. K. Makarov, S. N. Popova, “Local controllability of characteristic Lyapunov exponents of systems with simple exponents”, Differ. Uravn., 33:4 (1997),  495–499  mathnet  mathscinet; Differ. Equ., 33:4 (1997), 496–500
24. S. N. Popova, E. L. Tonkov, “Compatible systems and the control of Lyapunov exponents”, Differ. Uravn., 33:2 (1997),  226–235  mathnet  mathscinet; Differ. Equ., 33:2 (1997), 226–235
1995
25. S. N. Popova, E. L. Tonkov, “On the uniform compatibility of linear systems”, Differ. Uravn., 31:4 (1995),  723–724  mathnet  mathscinet; Differ. Equ., 31:4 (1995), 672–674
26. S. N. Popova, E. L. Tonkov, “Control of Lyapunov exponents of consistent systems. III”, Differ. Uravn., 31:2 (1995),  228–238  mathnet  mathscinet; Differ. Equ., 31:2 (1995), 209–218
1994
27. S. N. Popova, E. L. Tonkov, “Control of Lyapunov exponents of consistent systems. II”, Differ. Uravn., 30:11 (1994),  1949–1957  mathnet  mathscinet; Differ. Equ., 30:11 (1994), 1800–1807
28. S. N. Popova, E. L. Tonkov, “Control of Lyapunov exponents of compatible systems. I”, Differ. Uravn., 30:10 (1994),  1687–1696  mathnet  mathscinet; Differ. Equ., 30:10 (1994), 1556–1564

2019
29. A. A. Gryzlov, V. A. Zaitsev, D. M. Kinzebulatov, N. V. Latypova, V. P. Maksimov, N. N. Petrov, S. N. Popova, V. I. Rodionov, L. I. Rodina, Yu. M. Smetanin, D. L. Fedorov, “Vasilii Yakovlevich Derr. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019),  612–617  mathnet
30. A. P. Beltyukov, A. A. Gryzlov, D. V. Dyugurov, V. A. Zaitsev, N. N. Petrov, S. N. Popova, V. I. Rodionov, Yu. M. Smetanin, A. D. Yashin, “Nikolai Nikolaevich Nepeivoda. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:2 (2019),  295–298  mathnet  elib
2017
31. A. P. Beltyukov, A. A. Gryzlov, V. Ya. Derr, D. V. Dyugurov, A. I. Karpov, M. A. Klochkov, G. V. Merzlyakova, N. N. Petrov, V. N. Pishkov, S. N. Popova, V. I. Rodionov, “In memory of Galimzyan Gazizovich Islamov (02.02.1948–22.11.2017)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017),  634–642  mathnet  elib
32. A. A. Gryzlov, V. Ya. Derr, V. A. Zaitsev, N. I. Korobeinikova, N. V. Latypova, I. V. Men'shikov, N. N. Petrov, S. N. Popova, D. L. Fedorov, “Lyudmila Ivanovna Rodina. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017),  146–150  mathnet  elib
2014
33. I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov, “In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 4,  146–154  mathnet
2010
34. S. D. Buntov, N. I. Leonov, N. N. Petrov, A. V. Borisov, A. A. Gryzlov, V. Ya. Derr, A. I. Karpov, B. P. Kondratyev, S. N. Popova, “Evgenii Leonidovich Tonkov (on his seventieth birthday)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, 3,  3–9  mathnet  elib

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