Nonfragile H∞ filtering for discrete multirate time‐delayed systems over sensor networks characterized by Gilbert‐Elliott models

In this article, the nonfragile H∞ filtering problem is investigated for a class of discrete multirate time‐delayed systems over sensor networks. The probabilistic packet dropout occurs during the information transmissions among the sensor nodes in the sensor network characterized by the Gilbert‐Elliott model. In order to take the multirate sampling into account, the state updating period of the system and the sampling period of the sensors are allowed to be different. The variation of the filter gain is considered to reflect the physical errors with the filter implementation. The aim of this article is to design a set of nonfragile filters such that, in the presence of multirate sampling, time‐delays, and packet dropouts, the filtering error dynamics is exponentially mean‐square stable and also satisfies the H∞ performance requirement. By using the Lyapunov‐Krasovskii functional approach, a sufficient condition is derived, which ensures the exponential mean‐square stability and the H∞ performance requirement of the filtering error dynamics. Then, the filter gains are characterized in terms of the solution to a set of matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed filtering scheme.