Abstract
This paper proposes a new fuzzy adaptive exponential synchronization controller for uncertain time-delayed chaotic systems based on Takagi-Sugeno (T-S) fuzzy model. This synchronization controller is designed based on Lyapunov-Krasovskii stability theory, linear matrix inequality (LMI), and Jesen's inequality. An analytic expression of the controller with its adaptive laws of parameters is shown. The proposed controller can be obtained by solving the LMI problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed method.
Highlights
Chaos synchronization is an important subject both theoretically and practically, for applications requiring oscillations out of chaos, machine and building structural stability analysis, chaos generators design and so on
The synchronization problem for time delayed chaotic systems is investigated by several researchers 14–20
Motivated by the above discussions, the aim of this paper is to investigate the fuzzy adaptive exponential synchronization problem for time delayed chaotic systems with unknown parameters
Summary
Chaos synchronization is an important subject both theoretically and practically, for applications requiring oscillations out of chaos, machine and building structural stability analysis, chaos generators design and so on. In 26, 27 , fuzzy adaptive synchronization methods for chaotic systems with unknown parameters were proposed. In spite of these advances in T-S fuzzy model-based chaos control and synchronization, most works were restricted to chaotic systems without time-delay. To the best of our knowledge, for the fuzzy synchronization problem of time delayed chaotic systems, there is no result in the literature so far, which still remains open and challenging Motivated by the above discussions, the aim of this paper is to investigate the fuzzy adaptive exponential synchronization problem for time delayed chaotic systems with unknown parameters.
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