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Stability analysis of multi-agent system with leaders and time delays under Gaussian profiles

In this paper we consider stability analysis of a class of of Multi-agent system with leaders and time delays under Gaussian profiles. The leaders and the followers are included in the proposed system, and only the leaders have the knowledge about the environment. The emergent behavior of the system motion is the result of a balance between inter-individuals interactions and the simultaneous interactions of the system with their environment. The paper considers some condition under which it shows that for Gaussian attractant/repellent profiles the leaders and followers with time delays will aggregate and form a cohesive cluster of finite size in a finite time under some mild assumptions.