Reliable H∞ filtering for neutral systems with mixed delays and multiplicative noises

•A new Lyapunov–Krasovskii functional is introduced to account for discrete and distributed delays.•The neutral elements and multiplicative noises have been considered in the design of reliable H∞H∞ filter.•An LMI approach is developed to solve the reliable H∞H∞ filtering problem, where both mean-square stability and H∞H∞ constraints are simultaneously guaranteed.

This paper investigates the reliable H∞H∞ filtering problem for a class of neutral systems with mixed delays and multiplicative noises. The mixed delays comprise both discrete and distributed delays. And 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 and multiplicative noises, sufficient conditions for the existence of a reliable H∞H∞ filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieve a guaranteed H∞H∞ performance level. Then a linear matrix inequality (LMI) approach for designing such a reliable H∞H∞ filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.