On Effect of Communication Delay and Packet Reordering on Estimation and Control

Design of communication protocols for real time estimation and control is an important problem in cyberphysical systems. Control performance is dependent on both the throughput and the delay characteristics of the communication network. We consider the problem of estimation and control of a linear time-invariant process across a communication channel that stochastically introduces both a time-varying delay and an erasure event for the sensor data at every time step. Thus, the data may arrive at the receiver delayed and out of order, or may simply be lost. There are two contributions of this work. We prove that even if the delay distribution has an infinite support and the delays are correlated across time, the necessary and sufficient condition for stability depends merely on the erasure probability. We also show that performance of the plant can not be characterized through a few moments of the delay distribution. Thus, conjectures such as a delay distribution with lesser variance always yields better performance, as compared to a delay distribution with the same mean but larger variance, are incorrect.