39 How to check continuous system stability in the Lyapunov sense?

Problem: Check the stability (in Lyapunov sense) for the state coefficient matrix

$$A=% \begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ -1 & -2 & -3 \end{bmatrix}$$

We solve the Lyapunov equation using lyap() function in MATLAB and LyapunovSolve[] function in Mathematica, and then check that the solution is positive definite (i.e. all its eigenvalues are positive).

Mathematica solution.

Matlab solution.