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Chaotic secure communication with quadratic optimal performance via LMI-based observer design. (English)
Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 10, 3311-3322 (2010).
Summary: This paper considers an observer-based secure communication of chaotic systems with parameter mismatch, parametric perturbations and external disturbances on both transmitter and receiver systems. Based on the quadratic optimal control approach, a nonlinear observer is constructed to realize chaotic synchronization. The sufficient criterion for stability condition is formulated in two linear matrix inequality (LMI) forms. The error of the recovered message is then stated in an $H_{\infty }$ criterion. Using the proposed scheme, the global synchronization between the transmitter and the receiver can be obtained. Furthermore, the quadratic optimal and robust performance could be achieved in the chaos-based secure communication. Two numerical simulations of the Chua’s circuit and the Rössler system verify the effectiveness of the proposed scheme.