Frequency-domain performance analysis of distributed-parameter systems under periodic sampled-data feedback control

The stability and performance of distributed-parameter systems operating under periodic sampled-data feedback control is studied via integral-quadratic constraint (IQC) based analysis. Sufficient frequency-domain conditions are derived for verifying a specified bound on the L2-gain of 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 a finitedimensional LTI controller. The analysis is underpinned by a time-varying delay model of the sample-and-hold operation and IQC characterizations of a related system. An illustrative numerial example involving the control of a linear system of hyperbolic conservation laws is presented.