Lyapunov-based Fractional Order of Disturbance Observer and Sliding Mode Control for a Secure Communication of Chaos-based System

This paper proposes a new stability condition for a fractional order calculus (FOC)-based for the disturbance observer (DO) and sliding mode control (SMC) of a secure communication system (SCS). First, the mathematics of the chaotic system was remodeled into the Takagi-Sugeno fuzzy (TSF) with the aim of softening the calculation of control design and stability analysis. Second, the synchronization of two nonidentical chaotic systems was adopted by using a newly proposed Lyapunov-based stability condition. Third, a new disturbance observer was proposed based on the suggested stability condition together with the inversed model-based concept. To show the correction of the proposed method, the stability analysis was adopted to obtain the goal. Finally, the simulation by using MATLAB software was used to conduct the effectiveness of the proposed methods. The achievements are small tracking errors, stable steady-states, and all tested disturbances and uncertainties were mostly rejected.