10 / 11
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. «Естественные науки». 2016. № 3
25
19.
Фетисов Д.А.
Об одном методе решения терминальных задач для аффинных
систем // Наука и образование. МГТУ им. Н.Э. Баумана. Электрон. журнал.
2013. № 11. DOI: 10.7463/1113.0622543 URL:
http://technomag.bmstu.ru/doc/622543.html
REFERENCES
[1] Varga A. On solving periodic differential matrix equations with applications to
periodic system norms computation.
44th IEEE Conference on Decision and
Control 2005
;
European Control Conference CDC-ECC '05
, 2005, pp. 6545–
6550.
[2] Kyrchei I
.
Explicit formulas for determinantal representations of the Drazin
inverse solutions of some matrix and differential matrix equations.
Applied
Mathematics and Computation
, 2013, vol. 219, iss. 14, pp. 7632–7644.
[3] Lang N., Mena H., Saak J. On the benefits of the
LDL factorization for large-
scale differential matrix equation solvers.
Linear Algebra and its Applications
,
2015, vol. 480, pp. 44–71.
[4] Mori T., Fukuma N., Kuwahara M. On the Lyapunov matrix differential equation.
IEEE Transactions on Automatic Control
, 1986, vol. 31, pp. 868–869.
[5] Davis J.M., Gravagne I.A., Marks R.J., Ramos A. Algebraic and dynamic
Lyapunov equations on time scales.
Proceedings 42nd Southeastern Symposium
on System Theory
, Tyler, TX, 2010, pp. 329–334.
[6] Zhang J., Liu J.
New estimates for the solution of the Lyapunov matrix
differential equation.
Electronic journal of linear algebra
, 2010, vol. 20,
pp. 6–19.
[7] Yongliang Zhu, Pagilla P.R. Bounds on the solution of the time-varying linear
matrix differential equation
H
( ) = ( ) ( ) ( ) ( ) ( ).
P t
A t P t P t A t Q t
43rd IEEE
Conference on Decision and Control
, 2004, vol. 5, pp. 5392–5396.
[8] Hai-Jun Peng, Zhi-Gang Wu, Wan-Xie Zhong. Fourier expansion based recursive
algorithms for periodic Riccati and Lyapunov matrix differential equations.
Journal of Computational and Applied Mathematics
, 2011, vol. 235, iss. 12,
pp. 3571–3588.
[9] Nguyen T., Gajic Z. Solving the matrix differential Riccati equation: a Lyapunov
equation approach.
IEEE Transactions on Automatic Control
, 2010. vol. 55,
iss. 1, pp. 191–194.
[10] Gajic Z., Koskie S., Coumarbatch C. On the singularly perturbed matrix
differential Riccati equation.
Proceedings IEEE Conference Decision and
Control
, 2005, pp. 3638–3644.
[11] Kittipeerachon K., Hori N., Tomita Y. Exact discretization of a matrix differential
Riccati equation with constant coefficients.
IEEE Transactions on Automatic
Control
, 2009, vol. 54, iss. 5, pp. 1065–1068.
[12] Garrett C.K., Ren-Cang Li. GIP integrators for Matrix Riccati Differential
Equations.
Applied Mathematics and Computation
, 2014, vol. 241, pp. 283–297.
[13] Verde-Star L. On linear matrix differential equations.
Advances in Applied
Mathematics
, 2007, vol. 39, iss. 3, pp. 329–344.
[14] Bin Z., Guangren D. Closed form solutions for matrix linear systems using
double matrix exponential functions.
Control Conference CCC-2007
, 2007,
pp. 123–127.
[15] Ince E.L. Ordinary differential equations. London, N.Y., Longmans, Green and
Co., 1927. 558 p.
[16] Hartman P. Ordinary differential equation. N.Y., London, Sydney, John Wiley &
Sons, 1964. 612 p.