A necessary and sufficient condition for all the eigenvalues of a real matrix to have negative real parts is that the equation
has as a solution where is an matrix and is a positive definite quadratic form.
A necessary and sufficient condition for all the eigenvalues of a real matrix to have negative real parts is that the equation
has as a solution where is an matrix and is a positive definite quadratic form.
Weisstein, Eric W. "Lyapunov's First Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LyapunovsFirstTheorem.html