This paper deals with the global finite-time synchronization of a class of third-order chaotic systems with some intersecting nonlinearities, which cover many famous chaotic systems. First, a simple, continuous and dimension-reducible control by the name of the variable-substitution and feedback control is designed to construct a master–slave finite-time synchronization scheme. Then, a global finite-time synchronization criterion for the synchronization scheme is proven and the synchronization time is analytically estimated. Subsequently, the criterion and optimization technique are applied to the well-known brushless direct current motor (BLDCM) system and the classic Lorenz system, respectively, further obtaining some new optimized synchronization criteria in the form of algebra. Two numerical examples for the BLDCM system and a numerical example for the Lorenz system are simulated and analyzed to verify the effectiveness of the theoretical results obtained in this paper.

中文翻译：

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一类混沌系统的变量代换和反馈控制的全局有限时间同步

本文研究了一类具有交叉非线性的三阶混沌系统的全局有限时间同步问题，涵盖了许多著名的混沌系统。首先，设计了一个简单的、连续的、可降维的变量替代和反馈控制的控制，以构建一个主从有限时间同步方案。然后，证明了同步方案的全局有限时间同步准则，并分析估计了同步时间。随后，将该准则和优化技术分别应用于著名的无刷直流电机（BLDCM）系统和经典的Lorenz系统，进一步得到了一些新的代数形式的优化同步准则。