Fast Speed Convergent Stability of T-S Fuzzy Sliding-Mode Control and Disturbance Observer for a Secure Communication of Chaos-Based System

This article presents the fast convergent stability of disturbance observer (DO) and sliding mode control (SMC) for a secure communication of fractional-order chaotic-based system. First, the fractional-order is remodeled into a Takagi-Sugeno fuzzy (TSF) system with the aim of softening the calculations of observer and controller design. Second, the master and slave systems (MSSs) were synchronized by the fast convergent stability (FCS) sliding mode control with double phases of the same stability condition. Third, the disturbance observer was newly proposed for estimating the disturbance and uncertainty of the secure communication system (SCS). Fourth, the stability of the proposed method was archived via the Lyapunov condition. The MATLAB simulation with support of FOMCON tool box was used to validate the correction of the proposed control theory. The obtained results such as small tracking errors and small settling-times were used to confirm that the proposed theory is good at rejecting perturbations and used control method is good at synchronizing the chaotic systems.