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This technical note considers the consensus problem in high-order multiagent systems under undirected networks. By employing agents relative positions, sufficient conditions are proposed under which the agents reach agreement on a common position while their higher-order states converge to zero. Despite introduced consensus protocols in the literature for high-order systems, by using only relative positions, it is possible to achieve consensus on the average of any shared quantities of the agents. By setting the shared quantities properly, the obtained protocol is employed to achieve consensus on the average of the initial positions of the agents. Numerical examples confirm the accuracy of the proposed consensus protocol.
Rezaee et al. (Wed,) studied this question.