A Fuzzy Control Strategy to Synchronize Fractional-Order Nonlinear Systems Including Input Saturation

One of the most important engineering problems, with numerous uses in the applied sciences, is the synchronization of chaos dynamical systems. This paper introduces a dynamic-free T-S fuzzy sliding mode control (TSFSMC) method for synchronizing the different chaotic fractional-order (FO) systems, when there is input saturation. Using a new definition of fractional calculus and the fractional version of the Lyapunov stability theorem and linear matrix inequality concept, a Takagi-Sugeno fuzzy sliding mode controller is driven to suppress and synchronize the undesired behavior of the FO chaotic systems without any unpleasant chattering phenomenon. Finally, an example of synchronization of complex power grid systems is provided to illustrate the theoretical result of the paper in real-world applications.