H ∞ filtering for multi‐rate multi‐sensor systems with randomly occurring sensor saturations under the p ‐persistent CSMA protocol
Yuxuan Shen, Zidong Wang, Bo Shen, Fuad E. Alsaadi · IET Control Theory and Applications · 2020
In this study, the 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 filter such that the filtering error dynamics is exponentially mean‐square stable and the performance requirement is satisfied simultaneously. Sufficient conditions are established on the existence of the desired 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.