Frequency-Domain Analysis of Networked Control Systems Modeled by Markov Jump Linear Systems

This article addresses networked control systems that can be modeled by Markov jump linear systems, including linear control systems with correlated random delays and correlated random packet drops. The analysis focuses on the statistical moments (mean and variance) of the modeled system. It is first established that the map between the deterministic input of the system, and the statistical moments of the state and output can be described by a time-invariant system. This fact is then used to provide a frequency-domain analysis framework that allows for computing the mean and bounding the variance of the time response of the system to any deterministic input, based on a graphical method. For the special case of networked control systems with i.i.d. delays and drops, it is formally established that the variance bounds are tighter than the ones provided in the previous work. The results are applied to the remote control of a linear process. The delays are obtained experimentally in a setting where two remote processors communicate wirelessly using two XBee modules. Based on these experimental data, it is concluded that the delays associated with two consecutive transmissions are correlated. The provided tools are then used to analyze the input to output behavior of the system.