**AUTHORS:**Kepeng Han, Dongmei Xie

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**ABSTRACT:**
In this paper, we focus on studying the group consensus tracking issue of single-integrator and secondintegrator multi-agent systems with fixed communication topology and time delays under a pinning control protocol, respectively. For the former, We aim to propose some necessary and/or sufficient group consensus tracking conditions by using Lyapunov-Krasovskii function. For the latter, the observer-based bounded group consensus tracking control problem of second-order multi-agent systems in a disturbance environment is investigated, and some sufficient bounded group consensus tracking criteria are established. Moreover, this paper proposes a method of graph refactoring to find the relationship between the communication topology graph and matrix. Finally, numerical simulations are given to verify the effectiveness of our theoretical results.

**KEYWORDS:**
Multi-agent systems, group consensus tracking, pinning control, Lyapunov-Krasovskii function, distributed observer.

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