Frequency domain analysis of networked control systems modelled by Markov jump linear systems

This paper addresses networked control systems that can be modelled by Markov jump linear systems, including linear control systems with correlated random delays and correlated random packet drops. Our analysis focusses on the statistical moments (mean and variance) of the modelled system. We start by establishing 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. Then, we use this fact 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 independent and identically distributed delays and drops we formally establish that our variance bounds are tighter than the ones provided in previous work. We apply the results to the remote control of a linear process. We obtain the delays experimentally by having two remote processors communicate through two XBee modules