Frequency-domain stability criteria for distributed-parameter systems under periodic sampled-data feedback control

The stability of distributed-parameter systems operating under periodic sampled-data feedback control is studied via integral-quadratic constraints (IQCs). Simple sufficient frequency-domain stability criteria are derived for the feedback interconnection of a plant with (irrational) Callier-Desoer class transfer function and a feedback controller obtained via the periodic sample-and-hold discretization of an LTI controller with rational transfer function. The analysis is underpinned by a time-varying delay model of the sample-and-hold operation and IQC characterizations of a related system.