A NEW SOLUTION METHOD FOR THE DISCRETE LYAPUNOV EQUATIONS

Fang Yamin (P. R. China), Li Shuhong (P. R. China) and Zhang Mabiao (P. R. China)

Received December 2, 2007

Abstract

In this paper a new method for the discrete Lyapunov equations is presented. At first we assume that A can be diagonalized. So we can replace A and  by their eigenvalue decompositions. Then we can solve the transformed discrete Lyapunov equations easily. In the following we obtain the solutions of the original discrete Lyapunov equations by a simple linear transformation.

Keywords and phrases: discrete Lyapunov equation, eigenvalue decomposition, Krylov subspace, model-order reduction.