Stabilization Using Multiple Sensors over Analog Erasure Channels

Consider a discrete-time, linear time-invariant process, two sensors and one controller. The process is observed by the sensors, which are connected to the controller via links that can be modeled as erasure channels. If a link transmits successfully then a finite-dimensional vector of real numbers is conveyed from the sensor to the controller. If an erasure event occurs, then any information conveyed over the link is lost. This paper addresses the problem of designing the maps that specify the processing at the controller and at the sensors for stabilizing the process in the bounded second moment sense. When the information is lost over the links either in an independent and identically distributed (i.i.d.) or Markovian fashion over time, we derive necessary and sufficient conditions for the existence of maps such that the process is stabilized. Such conditions are expressed as inequalities involving the parameters of the plant and the probabilities of link fading, and provide the least conservative stabilization conditions. We also indicate how our approach can be used if more than two sensors are available, if the sensors can cooperate and if the acknowledgment signals are also transmitted over erasure channels. The analysis also carries over to the case when the single channels are replaced by networks of erasure channels.