The equation:
A'P + PA = -Q
where A is an n×n matrix, P is a symmetric positive-definite matrix of the same size, and Q is a symmetric positive-semidefinite matrix.
A is the matrix of the system.
I am trying to understand the lyapunov equation. Maybe it's a very stupid question. What does the matrix P represent? What is the origin of the equation? Why this prove the stability?