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

This brief investigates the <i>H</i><sub>∞</sub> 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 <i>H</i><sub>∞</sub> filter are derived, such that the filtering error dynamics is asymptotically mean-square stable and also achieves a guaranteed <i>H</i><sub>∞</sub> performance level. Then, a linear matrix inequality approach for designing such an <i>H</i><sub>∞</sub> filter is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.

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