A New Solution Method for the Lyapunov Matrix Equation

Abstract

The matrix equation $A^T P + PA = - Q$ is a useful equation for the study of the stability of a system when the dynamics are characterized by $\dot X = AX$. The matrix or system is stable if and only if the solution matrix P is positive definite for a positive definite matrix Q. This paper describes a new computational method of finding P when A and Q are known. The method is simple and efficient with matrix operations of the same order as A.