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.