Averaging‐Based Exponential Distributed State Estimation With Delays and Time‐Varying Networks

ABSTRACT The distributed state estimation problem for jointly observable linear systems undergoing time‐varying networks and communication delays is herein investigated. Two classes of delays are considered, that is, constant and time‐varying communication delays, whereas the time‐varying communication network satisfies the uniform connectivity on average assumption, thus also allowing disconnected communication topologies for . Our approach exploits a novel constructive approach for stability by averaging consisting of a delay‐free transformation and an innovative system presentation with rapidly‐varying scalar coefficients with zero average. Exponential stability results in the form of LMI are derived by means of the Lyapunov–Krasovskii method, which allows analytically finding the upper‐bound of both delays and small parameter —standing for the switching frequency of the communication topologies—preserving the stability.