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.

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