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Saleh Mobayen

Mobayen, S., Tchier, F. 
Synchronization of a class of uncertain chaotic systems with ‎Lipschitz nonlinearities using state-feedback control design: A ‎matrix inequality approach ‎
Synchronization of a class of uncertain chaotic systems with ‎Lipschitz nonlinearities using state-feedback control design: A ‎matrix inequality approach ‎
Abstract


This paper proposes a new state-feedback stabilization control technique for a class of ‎uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov ‎stabilization theory and linear matrix inequality (LMI) scheme, a new sufficient condition ‎formulated in the form of LMIs is created for the chaos synchronization of chaotic systems ‎with parametric uncertainties and external disturbances on the slave system. Using the ‎Barbalat’s lemma, the suggested approach guarantees that the slave system synchronizes to ‎the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the ‎proper feedback gain vector F is also provided. A new continuous-bounded nonlinear ‎function is introduced to cope with the disturbances and uncertainties and obtain a desired ‎control performance, i.e. small steady-state error and fast settling time. Several criteria are ‎derived to guarantee the asymptotic and robust stability of the uncertain master-slave ‎systems. Furthermore, the proposed controller is independent of the order of the system’s ‎model. Numerical simulation results are displayed with an expected satisfactory ‎performance compared to the available methods.‎

 

 

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