SOME PROPERTIES OF LYAPUNOV MAPPING

摘要

In this paper some properties and applications of the Lyapunov mapping are considered. First, we show the spectrums of the restrictions of the Lyapunov mapping on subspaces of symmetric and skew symmetric matrices. Secondly, the norm of theLyapunov mapping is investigated. In third part, Lyapunov mapping is used for the problem of common quadratic Lyapunov functions. Some generalizations of results in Ooba et al. 1997 a and b are obtained. Then norm estimation is used for common Lyapunovfunctions of a set of matrices.