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This study investigates the consensus control of linear multi‐agent systems with communication time delay. Upon exploring certain features of Laplacian matrix, optimal consensus control conditions are identified using semi‐discretisation method that develops a mapping of the system response in a finite‐dimensional state space. Consensus region and consensus boundary can be obtained by comparing the maximum absolute value of the mapping's eigenvalues with 1. Besides, minimisation of the maximum absolute value of the eigenvalues leads to optimal control gains representing fastest convergence speed. The proposed control only uses relative state information of the system. Numerical simulations validate the proposed control design and show the performance with different control gains and time delays.
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Sheng et al. (2013) studied this question.
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