H ∞ filtering for multi‐rate multi‐sensor systems with randomly occurring sensor saturations under the p ‐persistent CSMA protocol

In this study, the $H_{\infty }$H∞ filtering problem is studied for a class of discrete networked multi-rate multi-sensor systems with randomly occurring sensor saturations under the p-persistent carrier sense multiple access (CSMA) protocol. A set of mutually independent Bernoulli distributed white sequences is introduced to characterise the random occurrence of the sensor saturations. The p-persistent CSMA protocol is employed to decide which sensor is allowed to transmit its measurement to the filter at a certain time instant. By using the lifting technique, the multi-rate system is converted to a single-rate one for convenient analysis. The main purpose of the addressed problem is to design an $H_{\infty }$H∞ filter such that the filtering error dynamics is exponentially mean-square stable and the $H_{\infty }$H∞ performance requirement is satisfied simultaneously. Sufficient conditions are established on the existence of the desired $H_{\infty }$H∞ filters and the corresponding filter gains are then characterised by resorting to the feasibility of certain matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed filtering scheme.