Robust stability and performance analysis of sampled-data systems

The authors consider the robust stability and performance analysis of a general linear interconnection of a continuous-time plant and a discrete-time controller via sample-and-hold devices. They obtain necessary and sufficient conditions for the robust stability of the feedback system consisting of an uncertain plant represented as a known linear time-invariant model with a time-varying norm bounded uncertainty, and a shift-invariant discrete-time controller. These results show that the condition arising from the small gain theorem is necessary and sufficient when the uncertainties belong to a class of linear systems. Also, similar results are derived for the case of structured uncertainty. Both L₂ and L_∞ signal norms are considered. A robust performance analysis problem is solved by converting it to a robust stability analysis problem