An algebraic, distributed state observer for continuous‐ and discrete‐time linear time‐invariant systems with time‐varying communication graphs

Abstract

In this paper we address the problem of distributed state estimation of continuous-and discrete-time stable, LTI systems. The classical observer canonical form representation of the system dynamics is used to identify the observable states for each node (agent). The main novelty of our contribution is to obviate the need of the asymptotically (or finite-time) local Luenberger observers.Instead, following the generalized parameter estimation-based observer design approach, we use the state transition matrix of the system to translate the problem of reconstruction of the observable states into one of parameter estimation---namely, the initial conditions of the associated trajectory. Exploiting the local observability property of the agents we prove that, with a simple sample-and-hold or finite summation operation, it is possible to estimate these parameters algebraically. Consensus strategies are then used to fuse the parameter estimates of all agents to reconstruct the complete state vector. Asymptotic or finite convergence time of the observer are established for several scenarios for the graph, including time-varying, switching and with transmission delays.