Robustness Analysis of Control Laws in Complex Dynamical Networks Evoked by Deviating Argument

In recent years, robust performance of the system has been broadly studied as a trending topic among a vast array of scholars. This paper discusses the robustness of control laws for complex dynamic networks (CDNs) with a deviation argument. We design two categories of control laws (linear control law and nonlinear control law) for the undisturbed CDNs to achieve exponential synchronization. It is intractable to ascertain the range of the deviation function exactly. Hence, some corresponding sufficient criteria are put forward to ensure exponential synchronization of CDNs with deviation argument when control laws are not changed. By adopting the Gronwall–Bellman lemma and solving the transcendental equation, we can obtain the admissible upper limits of the deviating function, to keep the corresponding control laws. In comparison with previous research findings, robustness, deviating argument, and control laws are all considered in this study, which enhances the previous findings. Finally, two emulation examples verify the validity of the analysis.