A new reduced-order observer design for the synchronization of Lorenz systems

An exponential polynomial observer for synchronization of chaotic systems

“…A particular interest is the connection between the observers for nonlinear systems and chaos synchronization, which is also known as master-slave configuration [23,24]. Thus, chaos synchronization problem can be regarded as observer design procedure, where the coupling signal is viewed as output and the slave system is the observer [4,9,24]. In this configuration, the two coupled systems are identical and therefore identical synchronization occurs which means that the difference of master and slave state vectors converges to zero for t !…”

“…Among the publications dedicated to chaos synchronization, many different approaches can be found. We cite the papers [6][7][8][9][10] which propose the use of state observers to synchronize chaotic systems; in Refs. [11][12][13] use feedback controllers; in [14,15] use nonlinear backstepping control; in papers [16,17] consider synchronization time delayed systems; in works [18,19] consider directional and bidirectional linear coupling; papers [20,21] use nonlinear control; in papers [11,12] use active control, in [13,22] use adaptive control and so on.…”

Secure Communications and Synchronization via a Sliding-Mode Observer

“…For example, if the transmitter and receiver are set to the same chaotic structures, then parameter identification methods can be used to construct the chaotic receiver [10]; when there are uncertainties in synchronization (e.g., the transmitter is not known exactly, there is noise in the transmission line), the transmitter and the receiver could be established in the same fuzzy models. A fuzzymodel-based design method has been applied to reach synchronization [11]; stability analysis of observer-based chaotic communication with respect to uncertainties can be found in [9,12,15].…”

A Model-Free Sliding Observer to the Synchronization Problem Using Geometric Techniques

“…But it turns out that the corresponding stability analysis cannot be directly applied in situations with output noise (or mixed uncertainty). So it is still a challenge to suggest a workable technique to analyze the stability of identification error generated by sliding-mode-type (discontinuous nonlinearity) observers [4][5][6][7][8][9][10][13][14][15].…”