Number of positive eigenvalues of the solution to the discrete Lyapunov matrix equation
T. Mori, Norio Fukuma, M. Kuwahara · International Journal of Systems Science · 1988
It is known that the discrete Lyapunov matrix equation has a positive semidefinite symmetric solution under an appropriate condition. This note proves the fact that the number of positive eigenvalues of the solution is equal to the rank of the controllability matrix formed from the coefficient matrices.