Tensor Product Model Transformation Based Control and Synchronization of a Class of Fractional‐Order Chaotic Systems

Abstract

AbstractFractional‐order chaotic systems are the complex systems that involve non‐integer order derivatives. In this paper, tensor product (TP) model transformation‐based controller design for control and synchronization of a class of the fractional‐order chaotic systems is investigated. We propose a novel linear matrix inequality (LMI)‐based stabilization condition for fractional‐order TP models with a controller derived via a parallel distributed compensation (PDC) structure. In the controller design, the controlled system first is transformed into a convex state‐space TP model using the TP model transformation. Based on the transformed TP model, the controller is determined by solving the proposed LMI condition. To the best of our knowledge, this is the first investigation of TP model transformation based design in fractional‐order systems. Several illustrative examples are given to demonstrate the convenience of the proposed LMI condition and the effectiveness of the controller design.