Distributed Cooperative Full-State Observers for Discrete-time Linear Systems with Missing Data

Abstract

Recently, a distributed cooperative full-state observer for discrete-time linear systems, where it utilizes a consensus mechanism which enables local observers to exchange their estimates in an appropriate interval has been proposed. The behavior of its estimation error has been derived and a necessary and sufficient condition such that the error asymptotically converges to zero has been presented. In this paper, the behavior of the observer systems for a case where stochastically data missing will occur is considered. A simple model by using Bernoulli distribution is introduced to represent random data missing events. Based on the model including a stochastic factor, a necessary and sufficient condition is presented for the mean square stability of the correlation of estimate error. That means its estimation error converges to zero almost surely. Numerical examples are shown to illustrate the behavior of the observer systems where its estimation error converges to zero even if data missing occurs at random.