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Using a scalar driving signal, synchronization for a class of chaotic systems has been developed in this study. For chaotic systems characterized by nonlinearity, which depends only on the available output, a unified approach is developed by carefully extending the conventional adaptive observer design. For exactly known chaotic systems, an exponential convergence of synchronization is achieved in the large. When mismatched parameters are presented, this method performs the asymptotic synchronization of output state in the large. The convergence of the estimated parameter error is related to an implicit condition of persistent excitation (PE) on internal signals. From the broad spectrum characteristics of the chaotic driving signal, we reformulate the implicit PE condition as an condition on injection inputs. If this condition is satisfied, the estimated parameters converge to true values and exponential synchronization of all internal states is guaranteed. Two typical examples, including Duffing-Holmes system and Chua's circuit, are considered as illustrations to demonstrate the effectiveness of the adaptive synchronizer. Furthermore, the robustness of adaptive synchronization in presence of measurement noise is considered where the update law is modified. Finally, numerical simulations and DSP-based experiments show the validity of theoretical derivations. Index Terms--Adaptive observer, chaotic synchronization, persistent excitation.

This paper presents synthesis approaches for synchronization and secure communications of chaotic systems by using fuzzy model-based design methods. Many well-known continuous and discrete chaotic systems can be exactly represented by T-S fuzzy models with only one premise variable. According to the applications on synchronization and signal modulation, the general fuzzy models may have either i) common bias terms; or ii) the same premise variable and driving signal. Then we propose two types of driving signals, namely, fuzzy driving signal and crisp driving signal, to deal with the asymptotical synchronization and secure communication problems for cases i) and ii), respectively. Based on these driving signals, the solutions are found by solving LMI problems. It is worthy to note that many well-known chaotic systems, such as Duffing system, Chua's circuit, Rossler's system, Lorenz system, Henon map, and Lozi map can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either the fuzzy driving signal or the crisp driving signal. Finally, several numerical simulations are shown to verify the results. Index Terms--Chaotic synchronization, linear matrix inequality, T-S fuzzy models.

This paper proposes a fuzzy model-based chaotic encryption approach using synchronization. The cryptosystem uses T-S fuzzy models to exactly represent discrete-time chaotic systems into separate linear systems. Then the synchronization problem is solved using linear matrix inequalities. The advantages of this approach are: the general and systematic T-S fuzzy model design methodology suitable for well-known Luré type discrete-time chaotic systems; flexibility in selection of chaotic signals for cryptosystem secure key generator; and multiuser capabilities. Especially taking a chaotic superincreasing sequence as an encryption key enhances the chaotic communication structure to a higher-level of security compared to traditional masking methods. In addition, numerical simulations and DSP-based experiments are carried out to verify the validity of theoretical results. [ABSTRACT FROM AUTHOR]