Reducibility of Linear Differential Systems to Linear Differential Equations
Tóm tắt
Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is established. The preservation of the additional property of periodicity of coefficients is guaranteed, and for two-dimensional or complex systems the constancy of their coefficients is preserved. The differences in feasibility of asymptotic and generalized Lyapunov reducibility from Lyapunov one are indicated.
Tài liệu tham khảo
V. A. Zaitsev, “Global Attainability and Global Lyapunov Reducibility of Two- and Three-Dimensional Linear Control Systems with Constant Coefficients,” Vestn. Udmurt. Univ., Matem. 1, 31 (2003).
I. N. Sergeev, “Limit Values of Lyapunov Exponents of Linear Equations,” Differ. Uravn., 46 (11), 1664 (2010).
B. P. Demidovich, Lectures in Mathematical Theory of Stability (Nauka, Moscow, 1967) [in Russian].
I. N. Sergeev, “Control of Solutions to a Linear Differential Equation,” Vestnik Mosk. Univ., Matem. Mekhan., No. 3, 25 (2009).
I. N. Sergeev, “Oscillation, Rotatability, and Wandering Characteristic Indicators for Differential Systems Determining Rotations of Plane,” Vestnik Mosk. Univ., Matem. Mekhan., No. 1, 21 (2019).
B. F. Bylov, R. E. Vinograd, D. M. Grobman, and V. V. Nemytskii, Theory of Lyapunov Exponents and its Application to Stability Issues (Nauka, Moscow, 1966) [in Russian].
V. P. Basov, “Structure of Solutions in a Right Differential System,” Vestnik Leningr. Univ., No. 12, 3 (1952).
Yu. S. Bogdanov, “To the Theory of Linear Differential Equations,” Doklady Akad. Nauk SSSR 104 (6), 813 (1955).
D. M. Grobman, “Characteristic Indicators of Systems Close to Linear Ones,” Matem. Sbornik 30(72) (1), 121 (1952).