This paper focuses on the average consensus problem for the wireless sensor networks (WSNs) with fixed and Markovian switching, undirected and connected network topologies in the noise environment. Event-based protocol is applied to each sensor node to reach the consensus. An event triggering strategy is designed based on a Lyapunov function. Under the event trigger condition, some sufficient conditions for average consensus in mean square are obtained. Finally, some numerical simulations are given to illustrate the effectiveness of the results derived in this paper. 1. Introduction Wireless sensor network (WSN) has attracted significant attention as an emerging communication architecture. It has many practical applications in such areas as robotics, surveillance and environment monitoring, and information collection. A WSN can be viewed as a multiagent system (MAS) from a network-theoretic perspective. Each node represents a sensor and each edge performs information exchange between sensors. In some cases, the agreement is a common value which may be the average of the initial states of the system, is often called average consensus, and has wide application background in the areas such as formation control [1], distributed filtering [2], and distributed computation [3]. It means to achieve the accordance of the states of MAS. In [4], Olfati-Saber and Murray consider the average consensus control for the directed and undirected networks with fixed and switching topologies. In [5], Kingston and Beard extend the results of [4] to the discrete-time models and weakened the condition of instantaneous strong connectivity. In [6], Xiao and Boyd consider the distributed averaging consensus of the networks with fixed and undirected topologies. In [7], Q. Zhang and J. Zhang design a distributed consensus protocol to analyze the multiagent systems in uncertain communication environments including the communication noises and Markov topology switches. In [8], Wang et al. investigate the H consensus control problem for a class of discrete time-varying multiagent systems with both missing measurements and parameter uncertainties. Also, the distributed estimation problems over sensor networks have been widely discussed in [9–11]. For the node of the WSNs with limited energy, control over networks with limited resources is a challenging task. Consequently, the most important problem in WSN is the energy consumption, which is directly proportional to the transmit power of the information exchange between the sensors. The event-based control can facilitate the efficient
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