An Extended Kalman Filtering Approach to Nonlinear Time-Delay Systems: Application to Chaotic Secure Communications

An observer design problem for a class of nonlinear time-delay systems subject to white Gaussian noise is studied. The problem addressed is the design of a full-state observer based on the extended Kalman filter (EKF), in which two terms are added to the Riccati differential equation. One of those makes the system robust to noise influences, and the other one is utilized for dealing with the delayed state. A Lyapunov-Krasovskii functional is used for giving sufficient conditions for local stability of the reconstruction error dynamics. A hybrid chaotic cryptosystem procedure based on the n-shift cipher is combined with synchronization based on the EKF for developing a secure communication system. A semiconductor laser with optical feedback is employed as a chaotic signal generator in which a full-state estimation via the EKF is achieved.