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.

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.

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

• Institute of Mathematics, Information Technology and Physics, Udmurt State University, Izhevsk
• N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
• Udmurt State University, Mathematical Department