The Small Gain Theorem in the Context of Sampled-Data Systems

This paper is entirely devoted to analyzing robust control of sampled-data systems. For that, conditions for robust stability under static and dynamic norm-bounded uncertainty are presented and are all expressed through differential linear matrix inequality, a useful mathematical tool able to keep convex all problems to be dealt with. A suitable version of the celebrated small gain theorem (SGT) is then presented and proved in the context of sampled-data systems with inputs and outputs defined in both, continuous- and discrete-time domains. Some academic examples are solved to illustrate the theory and to put in evidence the computational burden needed to calculate their solutions. Since the SGT is only sufficient, the examples are used to discuss and evaluate its conservatism.