Abstract
ABSTRACTThis paper addresses the modulus consensus in a network of singularly perturbed systems, all of which own multi-time scales characteristics. The interactions among the agents are collaborative and antagonistic interactions, and it can been modelled by a signed directed graph. Also, the effect of time-varying delay has been taken into account when modelling the agent dynamics. Based on singularly perturbed decomposition method, Kronecker product technique and the comparison principle, several sufficient conditions are presented under which networked singularly perturbed time-varying delay systems with collaborative and antagonistic interactions achieve modulus consensus. Moreover, the upper bound of singular perturbation parameter is deduced explicitly. Two simulation examples are presented to illustrate the validity of the proposed results.
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