Robust adaptive synchronization of a class of chaotic systems via fuzzy bilinear observer using projection operator

This study focuses on the problem of robust adaptive synchronization of uncertain bilinear chaotic systems. A Takagi-Sugeno fuzzy bilinear system (TSFBS) is employed herein to describe a bilinear chaotic system. A robust adaptive observer, which estimates the states of the TSFBS, is also developed. Advanced adaptive laws using a projection operator are designed to achieve both the robustness for the external disturbances and the adaptation of unknown system parameters. A comparison with the existing observer shows that the proposed observer can achieve a faster parameter adaptation and a robust synchronization for an uncertain TSFBS with disturbances when the adaptive laws are utilized. The asymptotic stability and the robust performance of the error dynamics are guaranteed by some assumptions and the Lyapunov stability theory. We verify the effectiveness of the proposed scheme using examples of the generalized Lorenz system in various aspects.