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Because of the widespread use of MASs in robot network systems, rotorcraft-based unmanned aerial vehicle (RUAV) systems, flight systems, biochemical processes, jet engines and so on, consensus seeking in complex MASs has been pursued for several decades. Various excellent nonlinear technologies have been applied to controller design for MASs, such as neural network control, adaptive control, robust control and backstepping control. Furthermore, combined with some of these control methods, many considerable achievements have been obtained (Sader et al., 2021; Zhao, Tiao & You, 2022; Liu, Wang & Cai, 2021; Shen, Huo & Saab, 2021; Xiao & Dong, 2021). The authors proposed a new neuro-based distributed controller in (Liu, Hu & Li, 2023) to achieve formation cooperation for leader-follower MASs, and a novel Lyapunov function was built to eliminate the influence of state delays. The full-state feedback NNs containment controller was presented for robots with flexible joints while ensuring the security of the robot in (He, Yan & Sun, 2018). The new adaptive fuzzy tracking algorithm was reported in (Sun, Su & Wu, 2020; Zhou & Tang, 2020; Chang, Zhang & Alotaibi, 2020) for nonlinear switched systems. The major characteristics of these distributed control methods are summarized as follows: (i) the nonlinear functions were not required to be known or expressed as linear parametric models because of the strong approximation ability of NNs; (ii) the methods in (Liu, Wang & Cai, 2021; Shen, Huo & Saab, 2021; Xiao, & Dong, 2021) all related to a common issue of `computer explosion' resulting from repeated differentiations in the standard recursive backstepping process; and (iii) the number of adjusted parameters in (Liu, Hu & Li, 2023; He, Yan & Sun, 2018) was too large because it was dependent on the quantities of NN nodes. To overcome the weakness of (ii), the DSC technique was combined with backstepping control to design controllers for multiagent systems (Sun & Ge, 2022; Yang, Zhao & Yuan, 2022), stochastic systems (Chen, Yuan & Yang, 2022), and multi-input multioutput systems (MIMO) (Aghababa & Moradi, 2021). Meanwhile, the problem addressed in (iii) was resolved by taking the norm square's upper bound of the weight vector instead of the vector itself for estimation (Jiang, Su & Niu,2022; Shahvali & Askari, 2022); however, there were still too many parameters to be estimated. On the other hand, notably, unmodelled dynamic and uncertain perturbations widely exist in many industrial plants. Their existence can affect the control performance, even making it unstable. The existence of unmodelled dynamics that may cause system instability was first initiated in (Krstic, Sun & Kokotovic, 1996). Meanwhile, dynamic nonlinear damping design was introduced for linear input unmodelled dynamics to solve global asymptotic stability problems. Furthermore, nonlinear unmodelled dynamics were discussed in (Chang, Zhang, & Alotaibi, 2020), and stochastic cases were discussed in (Li, Li & Chen, 2015; Zhu, Liu & Wen, 2020). A fuzzy control strategy was proposed by constructing an auxiliary dynamical signal aimed at nonlinear systems limited to unmodelled dynamics in (Yang & Wang, 2016). The fuzzy self-adapting control approach has been discussed by integrating the small-gain approach into the backstepping technique focusing on stochastic systems under the constraint of unmodelled dynamics in (Sun, Su &Wu, 2020). Despite these achievements, to date, few studies have focused on tracking systems with existing networked communication, unmodelled dynamics and external perturbations.