Leader-following consensus of nonlinear multi-agent systems with mixed delays and uncertain parameters via adaptive pinning intermittent control

Abstract The paper studies leader-following consensus problem of multi-agent systems with mixed delays and uncertain parameters, where it is not necessary that the interaction diagraph is strongly connected or contains a directed spanning tree, and only a small fraction of followers can sense the leader’s state on some disconnected time intervals due to communication constraints. By utilizing the adaptive pinning intermittent control idea, a novel distributed control protocol is designed based only on local intermittent information, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that leader-following consensus can be reached if the measure of communication is larger than a threshold value, and the adaptive coupling strengths are provided with an exponential convergence rate, which will quickly converge to steady value. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.