A new inclusion criterion for the stability of interval matrices

A new Gersgorin-type result on the location of the eigenvalues of a given matrix has been proved. On the basis of the inclusions there established, in this paper a new method is proposed for analyzing the stability of a class of uncertain linear systems, characterized by an interval family of dynamical matrices. As a result a new bound to the real parts (moduli) of the eigenvalues of matrices in the interval family are obtained. This bound immediately provides a sufficient condition of stability and a way to compute an estimate of the stability margin, i.e. of the minimal destabilizing perturbation for the uncertain system. A huge number of numerical experiments have been carried out to compare the method here proposed to others based on Gersgorin-type regions. The results show that in several cases it gives less conservative estimates than the other ones, thus suggesting that it may be a useful tool for the analysis of uncertain systems