On the stability of interval matrices
Giuseppe Franzè, Luciano Carotenuto, P. Muraca · 2004
A new method is proposed for computing a lower bound to the stability margin of an interval matrix family, thus providing also a sufficient condition for stability. The method is based on Gershgorin's theorem and on the optimal selection of the eigenvectors of the nominal system: the optimization considerably improves previous bounds reported in literature. The analytical results make the solution extremely simple. Numerical experiments show that several problems involving uncertain systems can be solved efficiently by the proposed method, also in view of the comparisons with other methods proposed in the literature.