Robust control of a class of sampled-data systems with LTI uncertainties

The robust stability and robust performance in sampled-data control is studied for systems with LTI uncertainties. A class of problems is considered, which allows an exact characterization of robust stability of the sampled-data system in terms of the H-infinity norm of a finite-dimensional discrete transfer function. In the problem class certain assumptions on the product of the uncertainty weight and the anti-aliasing prefilter are imposed. In return, the robustness conditions can be stated in a particularly compact form, in which the robust stability and performance problems for LTI perturbations reduce to standard finite-dimensional discrete robust stability and performance problems. The robust stability condition for LTI uncertainties is also compared to the robustness condition based on the small gain theorem. The analysis provides a method to estimate the conservatism of the small gain robustness condition directly in terms of the anti-aliasing prefilter and frequency weights. As a by-product of this analysis a non-trivial class of sampled-data systems is identified for which the small gain theorem gives a non-conservative condition for robust stability to norm-bounded LTI uncertainties.