Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 183795, 14 pages
http://dx.doi.org/10.5402/2011/183795
Research Article

Solutions of Higher-Order Homogeneous Linear Matrix Differential Equations for Consistent and Non-Consistent Initial Conditions: Regular Case

Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

Received 7 March 2011; Accepted 20 April 2011

Academic Editor: T. Yamazaki

Copyright © 2011 Ioannis K. Dassios. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. L. Campbell, Singular systems of differential equations, vol. 1, Pitman, San Francisco, Calif, USA, 1980.
  2. S. L. Campbell, Singular systems of differential equations, vol. 2, Pitman, San Francisco, Calif, USA, 1982.
  3. G. I. Kalogeropoulos, Matrix pencils and linear systems, Ph.D. thesis, City University, London, UK, 1985.
  4. A. D. Karageorgos, Matrix pencils and linear systems, Ph.D. thesis, City University, London, UK, 1985.
  5. D. P. Papachristopoulos, Analysis and applications of linear control systems, Ph.D. thesis, University of Athens, Greece, 2008.
  6. T. M. Apostol, “Explicit formulas for solutions of the second-order matrix differential equation Y=AY,” The American Mathematical Monthly, vol. 82, pp. 159–162, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. I. Kalogeropoulos, A. D. Karageorgos, and A. A. Pantelous, “Higher-order linear matrix descriptor differential equations of Apostol-Kolodner type,” Electronic Journal of Differential Equations, vol. 2009, no. 25, pp. 1–13, 2009. View at Google Scholar · View at Zentralblatt MATH
  8. I. I. Kolodner, “On exp(tA) with A satisfying a polynomial,” Journal of Mathematical Analysis and Applications, vol. 52, no. 3, pp. 514–524, 1975. View at Google Scholar · View at Zentralblatt MATH
  9. R. F. Gantmacher, The theory of matrices I & II, Chelsea, New York, NY, USA, 1959.
  10. H.-W. Cheng and S. S.-T. Yau, “More explicit formulas for the matrix exponential,” Linear Algebra and its Applications, vol. 262, pp. 131–163, 1997. View at Google Scholar · View at Zentralblatt MATH
  11. I. E. Leonard, “The matrix exponential,” SIAM Review, vol. 38, no. 3, pp. 507–512, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Verde-Star, “Operator identities and the solution of linear matrix difference and differential equations,” Studies in Applied Mathematics, vol. 91, no. 2, pp. 153–177, 1994. View at Google Scholar · View at Zentralblatt MATH