how to actually use lyap(A,Q)

So, lyap(A,Q) finds the 'solution' of Lyapunov equation A(transpose)*P + P*A + Q = 0, where P and Q are positive semi-definite.

But how are we actually able to specify Q? I thought in reality, we are trying to find a Lyapunov 'candidate' rather than a solution, where P abd Q that is positive semi-definite, not that we already know the value of Q.

Any insights on this would very much be appreciated.

[Komal Rajana]

try:

A=[1 2;-3 -4];
Q=[3 1;1 1];
% A*x+x*A'+Q==0
x = lyap(A,Q);

[Sung-Wook Lee]

Thanks for the comment, Komal. But the question is basically asking practical use of this lyap function where Q and P are solution candidate, not a given matrix.

Answer 1

[Fernando Duarte López]

I have always used the identity matrix as Q.