TY - JOUR
T1 - Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control
AU - Humberto Pérez-Cruz, J.
AU - Tamayo-Meza, Pedro A.
AU - Figueroa, Maricela
AU - Silva-Ortigoza, Ramón
AU - Ponce-Silva, Mario
AU - Rivera-Blas, R.
AU - Aldape-Pérez, Mario
N1 - Publisher Copyright:
© 2019 J. Humberto Pérez-Cruz et al.
PY - 2019
Y1 - 2019
N2 - In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.
AB - In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.
UR - http://www.scopus.com/inward/record.url?scp=85070477844&partnerID=8YFLogxK
U2 - 10.1155/2019/4706491
DO - 10.1155/2019/4706491
M3 - Artículo
AN - SCOPUS:85070477844
SN - 1076-2787
VL - 2019
JO - Complexity
JF - Complexity
M1 - 4706491
ER -