Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances

Xiwang Dong, Jianxiang Xi, Zongying Shi and Yisheng Zhong

International Journal of Systems Science, 2013, vol. 44, issue 10, 1843-1856

Abstract: Practical consensus problems for general high-order linear time-invariant swarm systems with interaction uncertainties and time-varying external disturbances on directed graphs are investigated in this article. A dynamic consensus protocol with non-uniform time-varying delays is adopted to deal with the practical consensus problem. Using state space decomposition, practical consensus problems of a swarm system are converted into stability problems of a disagreement subsystem. Based on the Lyapunov–Krasovskii functional approach and the linear matrix inequality technique, sufficient conditions for swarm systems to achieve practical consensus are proposed where the time-varying external disturbance can be in L2 or L∞. Numerical simulations are presented to demonstrate theoretical results.

Date: 2013
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DOI: 10.1080/00207721.2012.670296

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