Synchronization of a Chaotic System with Line Equilibrium using a Descriptor Observer for Secure Communication

The problem of secure communication is considered for a chaotic system with hidden attractor, through the observer design approach for descriptor systems. By considering the transmitted signal as an additional state, the nonlinear system is rewritten as a semilinear rectangular descriptor system, for which an observer is constructed. The observer synchronization is feasible under some rank conditions on the system matrices, a common assumption on the nonlinearities and the feasibility of an LMI. The design scheme is showcased through numerical simulations.