Abstract
Active control is an effective method for making two identical Rossler and Chen systems be synchronized. However, this method works only for a certain class of chaotic systems with known parameters both in drive systems and response systems. Modification based on Lyapunov stability theory is proposed in order to overcome this limitation. An adaptive synchronization controller, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized in the presence of system's unknown constant parameters, is derived. Especially, when some unknown parameters are positive, we can make the controller more simple, besides, the controller is independent of those positive uncertain parameters. At last, when the condition that arbitrary unknown parameters in two systems are identical constants is cancelled, we demonstrate that it is possible to synchronize two chaotic systems. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.
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