Some Applications of the Lyapunov Matrix Equation

The matrix equation A'P+PA = –Q originates in the stabilityanalysis of the system of linear differential equations x =Ax by Lyapunov's direct method. Many other aspects of the stabilityof such systems and of related problems in matrix theory canalso be examined by this matrix equation. Some of these arediscussed in this paper and new applications to the stabilityof second order damped dynamic systems and to stable quasi-Jacobimatrices are given.