Robust stability and diagonal Liapunov functions

It is shown that diagonal Liapunov functions play an essential role in the robust stability problem of linear autonomous continuous and discrete-time systems in state-space form, subjected to a broad class of perturbations. The results obtained generalize a well-known result of Persidskii (1969) and are related to a variety of similar results in the literature. Techniques are suggested for the application of the results to the problem of evaluating robust stability bounds in different contexts. Several examples are given