$H_{\infty } $ Filtering for Network-Based Systems With Delayed Measurements, Packet Losses, and Randomly Varying Nonlinearities

The H_∞ filtering problem is investigated for a class of systems subject to varying nonlinearities caused by network environment, which are governed by a Bernoulli switched white sequence. The sensor measurement will be received with delays or even lost during the transmission to the remote filter through the network links. Due to the delayed measurements and packet losses, the data processing center/filter will receive one or multiple packets or nothing at each time instant (i.e., within one sampling period). Based on a recent developed model to describe the above-mentioned phenomena, a full-order H_∞ nonlinear filter is designed. Sufficient conditions for the existence of such a filter are obtained, such that for all possible randomly varying nonlinearities, delayed measurements, and packet losses, the filtering error dynamic is asymptotically mean-square stable and also achieves a prescribed H_∞ performance level. The filter gains are obtained by solutions to a set of linear matrix inequalities. A simulation example is presented to show the effectiveness of the developed filter.