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This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n À 1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches. IntroductionThe insertion of the communication network among agents makes the analysis and design of multi-agent systems more complex. One of the challenging problems associated with networked multi-agent systems is the influence of the sampling period. For second-order integrator multi-agent systems, if there exist static state feedback protocols solving the consensus problem of the continuous-time systems, under any sampling period there exist sampled-data state feedback protocols solving the consensus problem of the sampled-data systems (see Hayakawa, Matsuzawa, and Hara 2006). Even if the interaction topology is varying, the sampling period can be arbitrarily selected for second-order integrator multi-agent systems (Zhang and Tian 2010). The first question to be answered in this article is whether such a property holds for systems of general linear dynamical agents. Unfortunately, we will show, the answer is negative. The second question considered in this article is how to establish consensus conditions relating to the sampling period with protocol parameters and interaction topologies. Like the research on the first question there are some results on loworder integrator agent systems. For first-order systems, Olfati-Saber and Murray (2004) consider the fixed and connected undirected topology and point out that if the sampling period is less than the reciprocal of the maximum out-degree, the consensus

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