Asynchronous links that re-order samples: An L2 gain embedding

Abstract

An embedding of the uncertain time-varying delay associated with a class of asynchronous sampled-data links is devised in terms of the L2 gain of a related input-output operator. For links in the class considered, each output zero-order-hold update event occurs after an uncertain time-varying delay from a corresponding aperiodic input sampling event. The encapsulation of the effective link delay is parametrized by upper and lower bounds on the uncertain interval between sample events and the variable delay for the corresponding update events. The possibility of sample re-ordering at the output can arise when the update delay is allowed to vary freely within the specified bounds, which is acc..