Finite-Horizon $H_{\infty}$ State Estimation for Complex Networks With Uncertain Couplings and Packet Losses: Handling Amplify-and-Forward Relays

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed
$H_{\infty}$
performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired
$H_{\infty}$
state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.