Abstract The aim of this paper is to design a simple and continuous controller, named the variable substitution and feedback controller (VSFC), to investigate global finite-time synchronization of the chaotic gyrostat systems. By constructing the finite-time synchronization model for the master–slave gyrostat systems under the new designed VSFC, a finite-time synchronization criterion is presented with theoretically strict proof and the corresponding synchronization time is estimated by an explicit expression. Subsequently, applying the criterion and the optimization technique, some algebraic criteria with respect to various single VSFCs are further proven and optimized. Finally, three examples are presented to support the obtained results by comparing global asymptotic synchronization of the master–slave gyrostat systems under the VSC suggested in our previous work, with global finite-time synchronization of the master–slave gyrostat systems under the VSFC designed in this paper.

中文翻译：

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混沌陀螺系统全局有限时间同步模型与判据

摘要 本文的目的是设计一种简单且连续的控制器，命名为变量代换和反馈控制器（VSFC），以研究混沌陀螺系统的全局有限时间同步。通过构建新设计的VSFC下主从陀螺系统的有限时间同步模型，给出了有限时间同步准则，并在理论上严格证明，并通过显式表达式估计相应的同步时间。随后，应用该准则和优化技术，进一步证明和优化了关于各种单个 VSFC 的一些代数准则。最后，