Some Applications of the Lyapunov Matrix Equation

Abstract

The matrix equation A'P+PA = −Q originates in the stability analysis of the system of linear differential equations x = Ax by Lyapunov's direct method. Many other aspects of the stability of such systems and of related problems in matrix theory can also be examined by this matrix equation. Some of these are discussed in this paper and new applications to the stability of second order damped dynamic systems and to stable quasi-Jacobi matrices are given.