Uncertainties in Sampled Data Systems

The contributions of this paper are threefold. We first explore the differences in uncertainty representations and control designs between continuous time systems and discrete time systems, particularly the high frequency interpretation does not work for discrete time systems. It is shown that uncertainties appeared in sampled data systems may be highly structured, however they do not fall into any category which is currently available in the literature. Secondly, we define a measure on these uncertainties which confines a neighborhood to the nominal model in terms of frequency content, and then we propose a control design method which guarantees the stability of the closed loop system in the face of uncertainties. Last, we consider a generalization of a classical continuous time approach in representing the multiplicative uncertainty to sampled data systems by using a slightly modified sampler and present a method to calculate a frequency bound on the uncertainty in sampled data systems.