Abstract
This chapter studies practical consensus problems for general high-order linear time-invariant swarm systems with interaction uncertainties, nonuniform time-varying delays, and time-varying external disturbances on directed interaction topologies. A dynamic consensus protocol constructed by neighboring output information is adopted to deal with the practical consensus problem. Using the state space decomposition technique, practical consensus problems of swarm systems are converted into stability problems of disagreement subsystems. 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 \(L_2\) or \(L_\infty \). Explicit expressions of the practical consensus function and consensus error bounds are derived. Numerical simulations are presented to demonstrate the effectiveness of the obtained theoretical results.
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