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.
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
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
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; J. Math. Sci. (N. Y.), 230:5 (2018), 752–756
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
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
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
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
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
2012
9.
I. S. Zagrebina, S. N. Popova, “On Lyapunov exponents of the simplest time-lag equation”, Izv. IMI UdGU, 2012, 1(39), 54
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
11.
S. N. Popova, “Sufficient conditions of global attainability of linear control system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, 1, 73–80
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
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
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; 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; 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; 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; Differ. Equ., 39:2 (2003), 234–245
18.
S. N. Popova, “Local Attainability for Linear Control Systems”, Differ. Uravn., 39:1 (2003), 50–56; 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
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; 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; 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; 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; 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; 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; 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; 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; 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; Differ. Equ., 30:10 (1994), 1556–1564
2020
29.
S. N. Popova, “In memory of Evgeny Leonidovich Tonkov (1940–2014)”, Izv. IMI UdGU, 56 (2020), 3–4
2019
30.
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
31.
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
2017
32.
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
33.
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
2014
34.
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
2010
35.
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