Integral quadratic constraints for asynchronous sample-and-hold links

Abstract

A model is proposed for a class of asynchronous sample-and-hold operators that is relevant in the analysis of embedded and networked systems. The model is parametrized by characteristics of the corresponding time-varying input-output delay. Uncertainty in the relationship between the timing of zero-order-hold update events at the output and the possibly aperiodic sampling events at the input means that the delay does not always reset to a fixed value. This is distinct from the well-studied synchronous case in which the delay intermittently resets to zero at output update times. The main result provides a family of integral quadratic constraints that covers the proposed model. To demonstrate an application of this result, robust $\mathbf{L}_2$ stability and performance certificates are devised for an asynchronous sampled-data implementation of a feedback loop around given linear time-invariant continuous-time open-loop dynamics. Numerical examples are also presented.