Equivalence of stability concepts for discrete time‐varying systems

Stability concepts arising in the literature on absolute stability, difference inclusions and interval matrices are all shown to be equivalent to simultaneous asymptotic stability of a class of linear time‐varying discrete systems and, in turn, to exponential stability. This enables the classification of an interval matrix stability test due to Bauer et al. , a Lyapunov indicator test due to Barabanov and a constructive Lyapunov function test due to Brayton and Tong into a hierarchy of stability tests. Some applications of these tests are given and it is observed that they are not, in general, polynomial‐time tests.