A Distributed Observer for a Discrete-Time Linear System
This work provides a constructive method for distributed state estimation in linear systems, addressing the problem for control systems with sensor networks.
The paper presents a distributed observer for discrete-time linear systems with distributed outputs across a time-varying network, achieving exponential convergence of state estimation errors to zero at an arbitrarily chosen rate under strong connectivity.
A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to construct the local estimators which comprise the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. This is accomplished by exploiting several well-known properties of invariant subspaces plus several kinds of suitably defined matrix norms.