Exact Stability Analysis of Discrete-Time Linear Systems with Stochastic Delays

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Marcella M. Gomez, Wubing B. Qin, Gabor Orosz and Richard M. Murray
Submitted, 2014 American Control Conference (ACC)

This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are com- pared to those given by the mean dynamics. Our results reveal some fundamental limitations of connected cruise control which becomes more significant as the packet drop ratio increases.