Robustness of discrete systems under structured uncertainties

We give a sufficient condition for the robust stability of the discrete system X k+1, = (F + E)X k where the perturbation E is bounded (|E| ≤ U). A necessary and sufficient condition is derived in the case where F is a positive or a negative matrix and U = ∊|F|. The stability of interval matrices is also considered. Numerical examples are given for illustration.