Lyapunov Equation - Computational Aspects of Solution

Computational Aspects of Solution

The discrete Lyapunov equations can, by using Schur complements, be written as

$\begin{bmatrix} X^{-1} & A \\ A^H & X-Q \end{bmatrix}=0$

or equivalently as

$\begin{bmatrix} X & XA \\ A^HX & X-Q \end{bmatrix}=0$ .

Specialized software is available for solving Lyapunov equations. For the discrete case, the Schur method of Kitagawa (1977) is often used. For the continuous Lyapunov equation the method of Bartels and Stewart (1972) can be used.

Read more about this topic: Lyapunov Equation

Famous quotes containing the words aspects and/or solution:

“The happiest two-job marriages I saw during my research were ones in which men and women shared the housework and parenting. What couples called good communication often meant that they were good at saying thanks to one another for small aspects of taking care of the family. Making it to the school play, helping a child read, cooking dinner in good spirit, remembering the grocery list,... these were silver and gold of the marital exchange.”
—Arlie Hochschild (20th century)

“Who shall forbid a wise skepticism, seeing that there is no practical question on which any thing more than an approximate solution can be had? Is not marriage an open question, when it is alleged, from the beginning of the world, that such as are in the institution wish to get out, and such as are out wish to get in?”
—Ralph Waldo Emerson (1803–1882)