Abstract
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.