| The feedback linearization method based on differential geometry theory has been attracted more and more attention in the field of chaos control and synchronization in recent years.This method has shown the generality in the case of single input single output(SISO)for a variety of synchronization types,but the relative order needs to be expanded dynamically sometimes,because it often less than the system’s dimension for the groups selected from different input and output,otherwise,the full state feedback linearization cannot be achieved.More flexible applicability is shown in the case of the multiple inputs and multiple outputs(MIMO)in which more choices can be obtained.In this paper,the hybrid chaos synchronization between the identical structure chaotic systems is investigated in the case of the MIMO.Firstly,a brief introduction about mathematical basic knowledge of the differential geometry theory is given,including the concept of the vector field,the Lie derivative,the Lie bracket and the rules of their operation.In addition,the necessary and sufficient conditions for the solvability and the related theories for the full state feedback linearization in case of the MIMO system are summarized in detail.In the second chapter,the latest results of the typical literatures related to this paper’s research topic in recent years are introduced,such as the inverse full state hybrid projective synchronization which is researched based on the Lyapunov stability theory and the pole placement technique method,the control and synchronization between the systems based on the differential geometry method.In the third chapter,the process of the theoretical deduction for the hybrid synchronization based on the differential geometry method in the case of the MIMO are described in detail with the Lu system,Lorenz system and Chen system respectively.In which,the appropriate input position and output function are selected by the analysis of nonlinear characteristics for the affine error dynamical system,the involution of the corresponding distribution is examined,then the nonlinear coordinate transformation for the error dynamical system is carried out in which the corresponding Jacobi matrix is nonsingular.Finally,the hybrid synchronization between the two chaotic systems is achieved by combining the feedback linearization controller with outer loop control.The effectiveness of the proposed method was proved by the numerical simulation with the Matlab. |
