Abstract The problem of passivity-based sliding mode control is considered, for the unified chaotic system having uncertainties and perturbations. Using a combination between sliding mode method and the passivity method, an appropriate switching surface for the uncertain and perturbed system is designed, and then through passivity theory, the stability of the system is ensured. The proposed design is applied in two control problems, the first one being the stabilization of the uncertain perturbed unified chaotic system and the second one is the synchronization between two unified chaotic systems, where only the slave system contains uncertainties and perturbations. Finally, the effectiveness of the proposed methods are illustrated through numerical simulations, and also through a microcontroller implementation.

中文翻译：

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受扰不确定统一混沌系统基于无源性的滑模控制与同步

摘要 针对具有不确定性和扰动的统一混沌系统，考虑了基于无源性的滑模控制问题。采用滑模法和无源法相结合的方法，为不确定和受扰系统设计合适的切换面，然后通过无源理论保证系统的稳定性。所提出的设计应用于两个控制问题，第一个是不确定扰动统一混沌系统的镇定，第二个是两个统一混沌系统之间的同步，其中只有从系统包含不确定性和扰动。最后，通过数值模拟和微控制器实现说明了所提出方法的有效性。