Convergence of sampled-data models in digital redesign

This note proposes sufficient conditions that guarantee uniform-in-time convergence, as the sampling period approaches zero, of the control input to and the controlled output of a plant under sampled-data control to those corresponding signals of the same plant under continuous-time control. Sampled-data control systems exhibiting such behavior are formally defined as sampled-data models, which can be very convenient in the analysis and design of sampled-data systems since they can warn the engineer if a known limiting closed-loop behavior is likely to be violated. This practical consideration often occurs in digital redesign, where an analog control law is implemented digitally, with the objective of preventing intersample ripples.