An approach to robust performance analysis of sampled-data feedback control systems with aperiodic sampling and hold devices is developed. Such problems have been studied extensively for the case in which the feedback controller is static. In this note, the case of linear and dynamic feedback control is studied. An integral-quadratic-constraint-based (IQC) approach, which involves modelling the aperiodic sample-and-hold operation by a continuous-time time-varying delay operator and a loop transformation, is proposed to verify robust stability and performance for such systems. Semi-infinite frequency-domain criteria as well as the finite-dimensional time-domain counterparts are derived as the main results. Numerical examples are provided to evaluate the effectiveness of the proposed approach.