A Relation Between the Weighted Logarithmic Norm of a Matrix and the Lyapunov Equation

Author: Hu G-D.  

Publisher: Springer Publishing Company

ISSN: 0006-3835

Source: Bit Numerical Mathematics, Vol.40, Iss.3, 2000-01, pp. : 606-610

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Abstract

In this note, we define a weighted logarithmic norm for any matrix. In the case when a stable matrix A</i> is considered, we obtain the relationship between the maximal eigenvalue of a symmetric positive definite matrix H</i> which is a solution of the Lyapunov equation and the weight H</i> logarithmic norm of A</i>. It can be seen that the weighted logarithmic norm of A</i> is always a negative value in this case. Several examples illustrate the relationship.