Distributed observers for LTV systems: A distributed constructibility gramian based approach

Abstract

The paper addresses the problem of designing distributed observers for discrete linear time-varying (LTV) systems with distributed sensor nodes. It is shown, under the conditions of collective observability, strong connectivity of the sensor communication network, and invertibility of the state transition matrix, that the resulting observer yields exponential stability of the estimation errors with a pre-defined convergence rate and, in certain situations, requires the exchange of fewer data than other methods. It is shown that for linear time-invariant (LTI) systems this method yields fixed gains that can be computed in a few steps of a distributed algorithm with the underlying communication network. A design example is given where the asymptotic performance of the proposed observer is shown to be similar to that obtained using a distributed Kalman filtering approach.