Abstract
This paper is devoted to the consensus problem of networked nonlinear agents with multiple self-delays and time-varying coupling. We first establish a generalized Halanay's inequality based on comparison theorem, and then convert the consensus problem into a stability problem of retarded differential equation with time-varying coefficients, from which sufficient conditions for consensus are derived. Our results manifest that the time-average of coupling strength over intervals of certain length, together with the underlying topology and the values of self-delays, plays a crucial role in guaranteeing consensus. Based on the theoretical analysis, an estimation of the largest admissible delay is also available. This paper provides a general framework for achieving consensus in agents with time-varying coupling, such as coupling with external perturbations, intermittent control in on-off fashion, or pulse-modulated coupling strength, etc. Furthermore, useful criteria are given for various applications which have also been verified with numerical simulations.
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