Lyapunov Theorem

A method of checking the asymptotic stability of $\dot{x}=Ax$.

Theorem 5.5 page=187

The matrix $A$ is CT (?) stable if and only if for any given symmetric Positive-Definite Matrix $N$, the Lyapunov Equation

$$A^{T}M+MA=-N$$

has a unique symmetric solution $M$ and $M$ is as Positive-Definite Matrix