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Abstract
Motivated by the needs of multi-agent systems in the presence of sensing and communication which is delayed, intermittent, and asynchronous, we present a Kuramoto-type model as the delay inherent in such systems is taken into account. First, we have investigated a condition on maximum delay for the frequency entrainment of non-identical Kuramoto oscillators with heterogeneous delays and a constant coupling gain. Our next mission is to investigate the model of delayed coupled Kuramoto oscillators, which are characterized by non-identical natural frequencies and non-homogeneous coupling strength. We assume that the difference between the coupling gains is less than a certain limited value \(M\), and on the basis of Lyapunov stability theorem, we present a strictly positive lower bound for \(M\) to achieve a consensus on the derivatives of the phases. This consensus property is even more surprising because the phases themselves do not necessarily reach a consensus. We apply our results to these oscillators and show that synchronization is guaranteed for appropriate initial conditions.
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