Existence of positive solutions for generalized Lyapunov equations via a coupled fixed point theorem

Maher Berzig, Bessem Samet

We consider the generalized continuous-time Lyapunov equation: $$A^{\ast }XB+B^{\ast }XA=-Q,$$ where $Q$ is an $N\times N$ Hermitian positive definite matrix and $A,B$ are arbitrary $N\ti…