Chaotic synchronization based on Riccati inequality with application to secure communication

A systematic approach to construct two chaotically synchronized systems was developed. An object matrix was found to satisfy a Riccati inequality to design the synchronized chaotic Lipschitz state-observer through using the LMI (linear matrix inequality) toolbox. The proposed method, combining chaotic masking and chaotic modulation, was then applied to secure communication. The complex encrypted information signal was injected into the chaos system and simultaneously transmitted to the receiver after chaotic masking. The information signal was recovered through a complex decrypter in the synchronized receiver. Furthermore, the well-known Chua´s circuit was considered as illustration examples to demonstrate the effectiveness of the proposed approach.