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1. Introduction
Recent years have witnessed dramatic advances concerned with distributed coordination of multiple agents due to rapid developments of computer science and communication technologies. As an important issue of distributed coordination, the consensus problem has attracted more and more attention from researchers in various fields [1–5]. A special case of the issue is known as the leader-following consensus problems and has been investigated from different perspectives. Hong et al. in [6], for instance, designed distributed observers to track an active leader for second-order continuous multi-agents systems. Also, Tang et al. studied the leader-following consensus problem via sampled-data control in [7]. Besides, the authors in [8] explored first-order leader-following consensus algorithms under a directed fixed topology with a time-varying leader. Moreover, the results in [8] were furthered extended to the case of actuator saturation and switching topology in [9].
Due to the limited communication capacity, time delays are sometimes unavoidable in multiagent systems. Olfati-saber and Murray first analyzed the consensus problem with fixed undirected topology and time delays by a frequency domain approach in [1]. Based on the reduced-order Lyapunov-Krasovskii function and linear matrix inequalities (LMIs), Lin and Jia considered the averaged consensus problem with a switching topology and time-varying delays in [10]. In addition, Hu and Lin analyzed the second-order consensus problem for multiple agents with time-varying delays in terms of the Lyapunov-Razumikhin method in [11]. Note that [1, 10, 11] studied leaderless consensus problem with time delays. For leader-follower networks, Hu and Hong [12] investigated the second-order consensus problems with fixed and switching topologies with time delays, and Tang et al. generalized the results of [12] to the case of nonuniform time delays in [13], while the scenario in the presence of detectable time delays was addressed in [14]....