Event-Based $H_{\infty}$ Filter Design for a Class of Nonlinear Time-Varying Systems With Fading Channels and Multiplicative Noises

In this paper, a general event-triggered framework is developed to deal with the finite-horizon H
_∞
filtering problem for discrete time-varying systems with fading channels, randomly occurring nonlinearities and multiplicative noises. An event indicator variable is constructed and the corresponding event-triggered scheme is proposed. Such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not. The fading channels are described by modified stochastic Rice fading models. Some uncorrelated random variables are introduced, respectively, to govern the phenomena of state-multiplicative noises, randomly occurring nonlinearities as well as fading measurements. The purpose of the addressed problem is to design a set of time-varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a H
_∞
-norm in the mean-square sense. By utilizing stochastic analysis techniques, sufficient conditions are established to ensure that the dynamic system under consideration satisfies the H
_∞
filtering performance constraint, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired filter gains. Simulation results demonstrate the effectiveness of the developed filter design scheme.