Necessary and Sufficient Conditions for Robust Stability of SISO Sampled-data Systems to LTI Perturbations

SISO sampled-data systems are considered with stable, additive, LTI perturbations in the half-plane algebra to the continuous-time plant. Necessary and sufficient conditions are derived for robust L2 stability of such sampled-data systems. An example is provided to illustrate the results, and shows that the small gain theorem can be an extremely conservative robustness test in this sampled-data context.