Observing a linear process over analog erasure channels using multiple sensors: Necessary and sufficient conditions for mean-square stability

Consider a discrete-time linear time-invariant process being observed by two sensors, which are connected to an observer 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 sensors and the observer to calculate the minimum mean square error estimate of the state of the process. We derive necessary and sufficient conditions for the existence of maps such that the estimate error is bounded in the second moment sense.