A Distributed Observer for a Continuous-Time Linear System

Abstract

A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to design a gain g in 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. A linear inequality for g is provided when the network's graph is switching according to a switching signal with a dwell time or an average dwell time, respectively. It has also been shown the existence of g when the stochastic matrix of the network's graph is chosen to be doubly stochastic under arbitrarily switching signals. This is accomplished by exploiting several well-known properties of invariant subspaces and properties of perturbed systems.

A Distributed Observer for a Discrete-Time Linear System

“…The state estimator developed in this paper relies on an especially useful observation about distributed observer structure first noted in [11] and subsequently exploited in [12] and [15]. Just how much further this idea can be advanced remains to be seen.…”

“…Note that (14) holds because QP = 0. To understand why (15) is true, note first that ( (15) holds for q = 1; it follows by induction that (15) holds for any positive integer q.…”

“…With the growing interest in sensor networks and multiagent systems, the problem of estimating the state of a dynamical system whose measured outputs are distributed across a network has been under study in one form or another for a number of years [1]- [7]. Despite this, only quite recently have provably correct distributed state estimators begun to emerge which solve this problem under reasonably non-restrictive assumptions [8]- [15].…”

“…The same approach was simplified still further in [15] by exploiting certain well-known properties of invariant subspaces. There are however two distinct limitations of the types of estimators discussed in [11], [12], [15]. First, as they stand these estimators cannot deal with time-varying neighbor graphs.…”

Distributed Control of Linear Multi-Channel Systems

“…In the sequel it will be explained how to choose the K i , H ij , Ki and Hi so that the spectrum of ( 16) and ( 17) coincides with a prescribed symmetric set of complex numbers. To achieve this attention will first be focused on the properties of the open-loop error system described by (9) and…”