| The application of state feedback linearization method in the field of nonlinear control has been attracted more and more attention due to its peculiarity.In recent 10 years,the state feedback linearization method has been gradually introduced into chaos control and synchronization and the theory and application of single input single output(SISO)nonlinear systems is becoming more complete,but there are few articles on chaos synchronization in case of the multiple input multiple output(MIMO)for the various types of the chaotic systems due to its complexity.Therefore,the projective synchronization in the case of the MIMO is investigated by the state feedback linearization based on the differential geometry theory.In the first chapter,the related theories for the feedback linearization in the case of the SISO nonlinear systems and MIMO nonlinear systems based on the differential geometry theory are summarized particularly.In the second chapter,the typical literatures for the chaos control and synchronization researched in case of the SISO nonlinear systems is introduced in detail for recent years,such as the generalized projective synchronization based on state observer,nonlinear control of magnetic levitation systems using the differential geometry method,and the switched modified function projective synchronization of system with uncertain parameters etc.In the third chapter,the projective synchronization between two identical chaotic systems in the case of the MIMO is studied based on differential geometry method,and Lorenz system,Chen system and Liu system are taken as the examples.The necessary and sufficient conditions for the solvability of the full state feedback linearization is verified firstly,then after the nonlinear coordinate transformation and the full state feedback linearization are carried out,the controller is designed by which the projective synchronization is realized.Finally,the effectiveness of this method is demonstrated by simulations with Matlab. |
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