On Sampling Time and Invariance

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time. Understanding how invariant sets change with sampling time is critical for designing adaptive-sampling control schemes that ensure constraint satisfaction. We introduce M-step hold control invariance, a generalization of traditional control invariance, and show its practical use to assess the link between control sampling frequency and constraint satisfaction. We robustify M-step hold control invariance against model mismatches and discretization errors, paving the way for adaptive-sampling control strategies.