Event-Based $H_\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises

In this paper, the event-based finite-horizon <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called <inline-formula> <tex-math notation="LaTeX">$(x,v)$ </tex-math></inline-formula>-dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.