H∞ State Estimation for Two-Time-Scale Markov Jump Complex Networks Under Analog Fading Channels: A Hidden-Markov-Model-Based Method

In this paper, the asynchronous state estimation problem of two-time-scale Markov jump complex networks under analog fading channels is investigated, in which the mode of the designed state estimator is asynchronous to the system mode and the asynchronous probabilities are partially known. The two-time-scale phenomenon of complex networks is modeled by a singular perturbation parameter and the changes in connection mode between the complex networks are subject to a Markov chain. The output measurements are transmitted via analog fading channels and fading gains are used to represent the magnitude of the decline of the transmitted information. The purpose of this study is to design an asynchronous state estimator related to the asynchronous mode of the network topology such that the stochastic stability with an
$H_{\infty }$
performance index of the resultant error dynamics can be guaranteed. By designing the Lyapunov function which is associated with the singular perturbation parameter and the system mode, the stochastic stability condition of the estimation error system is derived. A new decoupling method to obtain the state estimator gains is proposed, which removes the limitation on the relaxation matrix of previous research results. Finally, the effectiveness of the methods are verified by a numerical simulation example and a capacitor-resistance circuit model.