Robust Stability of Multi-Hop Networks

We propose formal models for analyzing robustness of multi-hop control networks, where data from sensors to controllers and from controllers to actuators is sent through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors (errors with short time span), we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability (stability with probability one) in presence of transient link failures, and give efficient decision procedures. The last part of the paper deals with errors that have random time span. We show that, under some conditions, the permanent failure model can be used as a reliable abstraction.