Lyapunov equation

• May 13th 2009, 03:30 AM
inzaghina
Lyapunov equation
Hello...I searched very much on the web... examples for matrices A and C for the Lyapunov equation:

A* X + X * A' = C

do u have any suggestion?

thank you
• May 13th 2009, 07:29 AM
the_doc
Hello Inzaghina! If examples are all your looking for then the most trivial and easiest to find are to either set $A = I$ , the Identity matrix, or $X = I$. In the first case then you have that

$2X = C$

so choose any arbitrary X matrix and the $C$ is given by the above. In the second case you have that

$A + A^T = C$

so this time pick any matrix for A and then use the above to give you an example of $C$.

I have met this beast before but have to say that in my experience it's usually the case that you know $A$ and $C$ and need to find $X$!