Continuous Lyapunov equation
= Continuous Lyapunov equation
{c}
{title2=$AX+XA^T+Q=0$}
= Lyapunov equation
{c}
{synonym}
The continuous Lyapunov equation is $AX+XA^T+Q=0$. If every eigenvalue of $A$ has negative real part, it has a unique solution for each $Q$, and a positive-definite $Q$ gives a positive-definite $X$.