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Popova Svetlana Nikolaevna

Statistics Math-Net.Ru
Total publications: 28
Scientific articles: 25
Cited articles: 19
Citations in Math-Net.Ru: 96

Number of views:
This page:1544
Abstract pages:1646
Full texts:554
References:237
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:
  • Popova S. N., Tonkov E. L. Upravlenie pokazatelyami Lyapunova soglasovannykh sistem. I // Differentsialnye uravneniya. 1994. T. 30. # 10. S. 1687–1696.
  • Popova S. N., Tonkov E. L. Upravlenie pokazatelyami Lyapunova soglasovannykh sistem. II // Differentsialnye uravneniya. 1994. T. 30. # 11. S. 1949–1957.
  • Popova S. N., Tonkov E. L. Soglasovannye sistemy i upravlenie pokazatelyami Lyapunova // Differentsialnye uravneniya. 1997. T. 33. # 2. S. 226–235.
  • Makarov E. K., Popova S. N. O globalnoi upravlyaemosti polnoi sovokupnosti lyapunovskikh invariantov dvumernykh lineinykh sistem // Differentsialnye uravneniya. 1999. T. 35. # 1. S. 97–106.

http://www.mathnet.ru/eng/person18005
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. Spectral set of a linear system with discrete time
S. N. Popova, I. N. Banshchikova
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 132 (2017),  101–104
2. On the definition of uniform complete controllability
E. K. Makarov, S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017),  326–343
3. On the spectral set of a linear discrete system with stable Lyapunov exponents
I. N. Banshchikova, S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  15–26
4. On the property of uniform complete controllability of a discrete-time linear control system
V. A. Zaitsev, S. N. Popova, E. L. Tonkov
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  53–63
5. On the property of the closedness of the set of almost periodic functions
I. N. Banshchikova, S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  13–19
6. On Lyapunov exponents of the simplest time-lag equation
I. S. Zagrebina, S. N. Popova
Izv. IMI UdGU, 2012, no. 1(39),  54
7. Exponential stabilization of nonlinear control systems
V. A. Zaitsev, S. N. Popova, E. L. Tonkov
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  25–29
8. Sufficient conditions of global attainability of linear control system
S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 1,  73–80
9. Control over asymptotic invariants for the systems with almost periodic coefficients
S. N. Popova
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  117–118
10. Problems of control over Lyapunov invariants
V. A. Zaitsev, E. K. Makarov, S. N. Popova, E. L. Tonkov
Izv. IMI UdGU, 2006, no. 3(37),  43–48
11. Simultaneous Local Controllability of the Spectrum and the Lyapunov Irregularity Coefficient of Regular Systems
S. N. Popova
Differ. Uravn., 40:3 (2004),  425–428
12. Global Reducibility of Linear Control Systems to Systems of Scalar Type
S. N. Popova
Differ. Uravn., 40:1 (2004),  41–46
13. Global Controllability of the Complete Set of Lyapunov Invariants of Periodic Systems
S. N. Popova
Differ. Uravn., 39:12 (2003),  1627–1636
14. Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 39:2 (2003),  217–226
15. Local Attainability for Linear Control Systems
S. N. Popova
Differ. Uravn., 39:1 (2003),  50–56
16. On global controllability of the complete set of Lyapunov invariants for periodic systems
S. N. Popova
Izv. IMI UdGU, 2002, no. 2(25),  79–80
17. On the equivalence of local admissibility and complete controllability of linear systems
S. N. Popova
Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 6,  50–53
18. On the global controllability of a complete set of Lyapunov invariants of two-dimensional linear systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 35:1 (1999),  97–106
19. On the global controllability of central exponents of linear systems.
E. K. Makarov, S. N. Popova
Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 2,  60–67
20. Local controllability of characteristic Lyapunov exponents of systems with simple exponents
E. K. Makarov, S. N. Popova
Differ. Uravn., 33:4 (1997),  495–499
21. Compatible systems and the control of Lyapunov exponents
S. N. Popova, E. L. Tonkov
Differ. Uravn., 33:2 (1997),  226–235
22. On the uniform compatibility of linear systems
S. N. Popova, E. L. Tonkov
Differ. Uravn., 31:4 (1995),  723–724
23. Control of Lyapunov exponents of consistent systems. III
S. N. Popova, E. L. Tonkov
Differ. Uravn., 31:2 (1995),  228–238
24. Control of Lyapunov exponents of consistent systems. II
S. N. Popova, E. L. Tonkov
Differ. Uravn., 30:11 (1994),  1949–1957
25. Control of Lyapunov exponents of compatible systems. I
S. N. Popova, E. L. Tonkov
Differ. Uravn., 30:10 (1994),  1687–1696

26. Lyudmila Ivanovna Rodina. To anniversary
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
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017),  146–150
27. In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)
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
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  146–154
28. Evgenii Leonidovich Tonkov (on his seventieth birthday)
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
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  3–9

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