Reference state tracking in distributed leader-following wireless sensor networks with limited errors

In this paper, the limited error tracking problem is investigated for distributed leader-following wireless sensor networks (LFWSNs), where all sensors share data by the local communications, follower sensors are influenced by leader sensors directly or indirectly, but not vice versa, all sensor nodes track a reference state that is determined by the states of all leader sensors, and tracking errors are limited. In a LFWSN, the communicating graph is mainly expressed by some complete subgraphs; if we fix subgraphs that are composed of all leaders while all nodes in complete subgraphs of followers run on the sleeping-awaking method, then the fixed leaders and varying followers topology is obtained, and the switching topology is expressed by a Markov chain. It is supposed that the measurements of all sensors are corrupted by additive noises. Accordingly, the limited error tracking protocol is proposed. Based on the theory of asymptotic boundedness in mean square, it is shown that LFWSN keeps the limited error tracking under the designed protocol.