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Abstract
This article addresses the distributed consensus problem of linear multi-agent systems with discontinuous observations over a time-invariant undirected communication topology. Under the assumption that each agent can only intermittently share its outputs with the neighbours, a class of distributed observer-type of protocols are designed and utilised to achieve consensus. By using appropriate matrix decomposition, it is shown that consensus in the closed-loop multi-agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent. From a multiple Lyapunov functions approach, it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value. Furthermore, a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected. Particularly, the questions of what kind of agents and at least how many agents should be pinned are addressed. The effectiveness of the analytical results is finally verified by numerical simulations.
Acknowledgements
The authors sincerely thank the Associate Editor and all the anonymous reviewers for their valuable comments which helped them improve the manuscript of this paper. This work was supported by the Hong Kong Research Grants Council under the GRF Grant CityU 1114/11E, the National Nature Science Foundation of China under Grants 60974078, 90916003, 61104153, the China Postdoctoral Science Foundation under Grants 20100480211, 201104059 and the Information Processing and Automation Technology Prior Discipline of Zhejiang Province-Open Research Foundation under Grant 20120801.