Computational method to analyse the stability of interval matrices

A method is proposed to compute a lower bound to the stability margin of an interval matrix family, thus also providing a sufficient condition for stability. The method is based on Gershgorinʹs theorem and on the optimal selection of the eigenvectors of the nominal system; the optimisation considerably improves previous bounds reported in the 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 as compared to other methods proposed in the literature.