Synchronization of Rossler chaotic system for secure communication via descriptor observer design approach

An observer construction method for semilinear descriptor systems of the form Eẋ = Ax + f, where E (singular), A are linear operators and f is a nonlinear function, is studied. Using a new approach, based on matrix theory, it is shown that an observer may be designed under certain conditions on system operators if one linear matrix inequality (LMI) is satisfied. By treating the transmitted signal as an extra state, chaotic Rössler system is rewritten in the semilinear descriptor system form and then using proposed observer the transmitted signal is retrieved. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.