Oguzer SİNAN, Sefa BAYDAK, Ahmet DUMAN, Kemal AYDIN

Computation of the Solutions of Lyapunov Matrix Equations with Iterative Decreasing Dimension Method

ISSN: 2645-8845
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2018
Yayıncı: Fuat USTA

The existence of a solution of continuous and discrete-time Lyapunov matrix equations was studied. Both Lyapunov matrix equations are transformed into a matrix-vector equation and the solution of the obtained new system was examined. The iterative decreasing dimension method (IDDM) was implemented for solving the generated matrix-vector equation. Computations have been done with Maple procedures that run the constituted algorithms.

Keywords:

Hurwitz stability, IDDM, Lyapunov matrix equations, Schur stability,

PDF

___

[1] O. Akın, H. Bulgak, Linear Difference Equations and Stability Theory [in Turkish], Selc¸uk University, Research Center of Applied Mathematics, Konya, 1998.
[2] H. Bulgak, Pseudo Eigenvalues, Spectral Portrait of a Matrix and Their Connections with Different Criteria of Stability, In: Error control in Adaptivity in Scientific Computing, H. Bulgak, C. Zenger (editors), NATO Science Series, Kluwer Academic Publishers, 1999, (pp. 95-124).
[3] G. Alexander, Kronecker Products and Matrix Calculus with Applications, John Wiley & Sons, N.Y, 1981.
[4] G. H. Golub C. F. VanLoan, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 2013.
[5] K. Aydın, G. C. Kızılkan, A. O. C¸ ıbıkdiken, Generalized iterative decreasing method, European J. Pure Appl. Math., 3(5)(2010), 819-830.
[6] T. Keskin, K. Aydın, Iterative decreasing dimension algorithm, Comput. Math. Appl., 53(1)(2007), 1153-1158.
[7] H. Vang, J. Jiang, Solution of the system of linear algebraic equations by decreasing dimension, Appl. Math. Comput., 109(1)(2000), 51-57.