A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts (FOC) systems with mismatched uncertainties and disturbances. The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors. A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer. The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer. Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory. It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics. The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme. The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system. The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.

基于给定类别的具有不确定性和干扰不匹配的分数阶Colpitts（FOC）系统的被动同步，设计了鲁棒的多项式观测器。提出的观察者的主要目的是最小化未知的有界干扰对误差估计的影响。使用自适应多项式状态观测器，提出了一种更实用的输出反馈无源控制器。考虑使用FOC连续频率的分布式方法来分析观察者的稳定性。然后，基于分数Lyapunov稳定性理论，使用Finsler引理导出了鲁棒无源同步的一些严格条件。结果表明，所提出的方法不仅保证了控制器的渐近稳定性，而且允许导出的自适应律消除了非线性装置动力学中的不确定性。PSpice中详细介绍了使用无源性的整个系统，以证明所提出的控制方案的可行性。使用计算机仿真来说明分数阶混沌Colpitts系统的控制问题，从而说明了本研究的结果。所提出的方法描绘了针对一类带有分数导数的非线性系统的有效且系统的控制程序。使用计算机仿真来说明分数阶混沌Colpitts系统的控制问题，从而说明了本研究的结果。所提出的方法描绘了针对一类带有分数导数的非线性系统的有效且系统的控制程序。使用计算机仿真来说明分数阶混沌Colpitts系统的控制问题，从而说明了本研究的结果。所提出的方法描绘了针对一类带有分数导数的非线性系统的有效且系统的控制程序。