Abstract
In this paper, second-order multi-agent systems with intentionally induced delay are studied, which cannot achieve consensus with a non-delay position-based protocol. Under the proposed distributed protocol with the current and outdated position states, the crossing frequencies and crossing delays of the related quasipolynomial of the delayed systems are identified. By determining the crossing directions of the imaginary roots, the change of the number of the right half-plane roots can be obtained. Accordingly, consensus condition and consensus delay range are provided. Simulations illustrate the effectiveness of the theoretical analysis.
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