Robust stability and diagonal Lyapunov functions

This paper shows 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 and are related to a variety of similar results in the literature. Techniques are suggested for applying the results to the problem of evaluating robust stability bounds in different contexts. Several examples are given.