Mean-Square Stability of a Networked Feedback System with Random Data Transmission Delays

This work studies the mean-square stability of a discrete-time networked linear feedback system over a communication channel with random data transmission delays or packet dropouts. To describe data transmission process in the channel, a new stochastic state-space model is established for the unreliable channel. By applying this model, a set of necessary and sufficient conditions is presented for the mean-square stability of the networked feedback system. These conditions explain the interaction between the state-space model of the networked system and the statistics of the random parameters in the channel model in the mean-square stability problem. Moreover, we study the connection between the mean-square stability and input-output meansquare stability of this system. It is found that the mean-square stability criteria presented in this work is equivalent to the input-output mean-square stability criterion presented in our previous works.