Reliable H ∞ Filtering for Mixed Time‐Delay Systems with Stochastic Nonlinearities and Multiplicative Noises

This paper investigates the reliable H_∞ filtering problem for a class of mixed time‐delay systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time‐varying and distributed delays. The stochastic nonlinearities in the form of statistical means cover several well‐studied nonlinear functions. The multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. In the presence of mixed delays, stochastic nonlinearities, and multiplicative noises, sufficient conditions for the existence of a reliable H _∞ filter are derived, such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a guaranteed H _∞ performance level. Then, a linear matrix inequality (LMI) approach for designing such a reliable H _∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.