Stability analysis of a family of matrices

The authors extend the use of the Lyapunov equation method to check the stability of a family of matrices. The family of interval matrices is defined as the convex hull of a finite number of matrices and is a special case where each element has independent perturbation. While the stability of interval matrices cannot be inferred from the stability of its vertex matrices, the authors show that the family of matrices will be stable if the symmetric matrices associated with the vertex matrices have matrix measures less than two