Abstract
The leader-following guaranteed-performance consensus problems for second-order multi-agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results.
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