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Lyapunov equation
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. In particular, the discrete-time Lyapunov equation (also known as Stein equation) for X {\displaystyle X} is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is A X + X A H + Q = 0 {\displaystyle AX+XA^{H}+Q=0} .