Please how to Matrix Lyapunov equation?

Hello everyone,

I have one question, please can you tell me how I can solve the Matrix Lyapunov equation using Matlab or Wolfram Mathematica :

and this differential matrix equation: .

Thank you.

Answer 1

[Sam Chak]

Hi @Abdelkader Hd

You can use the function lyap to compute the solution to the Lyapunov equation. See the following example:

A = [0 1 0; -1 -2 0; 0 1 -1]
D = 2*eye(3)
X = lyap(A, D)
A*X + X*A'	% check: should be the same as –D

https://www.mathworks.com/help/control/ref/lyap.html