$H_{\infty }$ Filtering for Neutral Systems With Mixed Delays and Multiplicative Noises

This brief investigates the H_∞ filtering problem for a class of neutral systems with mixed delays and multiplicative noises. The mixed delays comprise both discrete time-varying and distributed delays. Moreover, the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays and multiplicative noises, sufficient conditions for the existence of an 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 approach for designing such an H_∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.