Many systems in the natural and physical world often work in unison with similar other systems. This process of simultaneous operation is known as synchronization. In the past few decades, owing to this phenomenon’s importance, extensive research efforts have been made. However, many of the existing results consider the systems are identical and/or linear time-invariant, while practical systems are often nonlinear and nonidentical for various reasons. This observation motivated several recent studies on the synchronization of nonidentical (i.e., heterogeneous) nonlinear systems. This paper summarizes some recent results on the synchronization of heterogeneous nonlinear systems, as developed in the thesis (Ahmed 2016). First, the results on the synchronization of a particular class of robustly stable nonlinear systems are presented. Then, these results are applied to an example model known as Brockett oscillator. Finally, using the Brockett oscillator as a common dynamics, output oscillatory synchronization results are given for heterogeneous nonlinear systems of relative degree 2 or higher. An application example of Brockett oscillator for power-grid synchronization is also presented. Some outlooks are provided regarding future research directions.

自然和物理世界中的许多系统通常与类似的其他系统协同工作。这种同时操作的过程称为同步。在过去的几十年中，由于这种现象的重要性，人们进行了广泛的研究工作。然而，许多现有结果认为系统是相同的和/或线性时不变的，而实际系统由于各种原因往往是非线性和不相同的。这一观察激发了最近关于非相同同步的几项研究（即，异构）非线性系统。本文总结了论文 (Ahmed 2016) 中开发的异构非线性系统同步的一些最新成果。首先，介绍了特定类别的鲁棒稳定非线性系统的同步结果。然后，将这些结果应用于称为 Brockett 振荡器的示例模型。最后，使用 Brockett 振荡器作为公共动力学，给出了相对度为 2 或更高的异构非线性系统的输出振荡同步结果。还介绍了用于电网同步的 Brockett 振荡器的应用示例。对未来的研究方向提供了一些展望。