New inclusion criterion for the stability of interval matrices

New results on the regions that include the spectrum of a given matrix have recently appeared in the literature. On the basis of the inclusions established, a new method is proposed for analysing the stability of a class of uncertain linear systems characterised 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 is obtained, which provides a sufficient condition of stability and a way to compute an estimate of the minimal destabilising perturbation (stability margin). The evaluation of this bound, as well as of other ones obtained by Gersgorin regions, is computationally simple and does not suffer from dimensionality problems. Then, the method can be used also when less conservative approaches (exploration of vertices and joining segments) require prohibitive computational efforts. Moreover, numerical comparisons, carried out on a large number of randomly generated interval matrices, show that the bound proposed here is inferior in about 3% and superior in about 25% in comparison to the results of a recently published Gersgorin-type method (Carotenuto et al., 2004).