Mean-square stabilizability of a SISO linear feedback system over a communication channel with random delay

This paper investigates the mean-square stabilizability of a networked discrete-time linear feedback system with multi-step random delay induced by a communication channel. It is assumed that the probability mass function (PMF) of the random delay is known. According to this model, an averaged channel transfer function and the spectral density of the channel uncertainty caused by the delay are obtained. A necessary and sufficient condition for mean-square stabilizability is presented. Due to the fact that a channel with random delay is with a finite impulse response, the stochastic uncertainty in the channel is a color noise. It is turned out that the mean-square stabilizability of the system is determined by the interaction between the spectral density of the channel uncertainty, the averaged channel transfer function and the plant in the closed-loop system. Finally, numerical examples are presented to illustrate the results in this work.