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:

“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)

“I herewith commission you to carry out all preparations with regard to ... a total solution of the Jewish question in those territories of Europe which are under German influence.... I furthermore charge you to submit to me as soon as possible a draft showing the ... measures already taken for the execution of the intended final solution of the Jewish question.”
—Hermann Goering (1893–1946)