IJPAM: Volume 53, No. 1 (2009)

SYLVESTER MATRIX DIFFERENTIAL EQUATIONS:
ANALYTICAL AND NUMERICAL SOLUTIONS

Laurene V. Fausett
Department of Mathematics
Texas A&M University-Commerce
Commerce, TX 75429, USA
email: [email protected]


Abstract.This paper considers the relationships between the general solution of the first-order matrix Sylvester ODE:

\begin{displaymath}\mathbf{X}'=\mathbf{A}(t)\mathbf{X}(t)+\mathbf{X}(t)\mathbf{B}(t) \end{displaymath}

in terms of two fundamental matrix solutions of $ \mathbf{T}' = \mathbf{A} \mathbf{T} $ and $ \mathbf{T}' = \mathbf{B}^*\mathbf{T}$, and the numerical solution of such equations which can be obtained using standard Matlab routines for the solution of vector ODE.

Theoretical results regarding the solution of a Sylvester control system

\begin{displaymath}\mathbf{X}' =\mathbf{A}(t)\mathbf{X}(t)+\mathbf{X}(t)\mathbf{B}(t) +\mathbf{C}(t)\mathbf{U}(t) \end{displaymath}

are used to compute the control signal $ \mathbf{U}(t) $, a particular solution, and the total controlled solution.

Received: March 30, 2009

AMS Subject Classification: 34H05, 93B05, 65L99

Key Words and Phrases: matrix differential equations, numerical solutions of ODE, fundamental matrix solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 1