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This paper studies the application of the observerbased chaos synchronization in the so-called Generalized Lorenz systems to secure encryption. More precisely, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data is proposed. Recall, that the classical CSK method determines the correct value of binary signal through checking which unsynchronized system is getting synchronized. On the contrary, our novel method, called as the Anti-Synchronization Chaos Shift Keying (ACSK) method, determines wrong value of binary signal through checking which already synchronized system is loosing synchronization. Even when using two very close each to other chaotic systems, the anti-synchronization is thousand times faster than synchronization. As a consequence, unlike the classical CSK, the method proposed here requires very reasonable amount of data to encrypt and time to decrypt a single bit. Moreover, its security can be systematically investigated showing its good resistance against typical decryption attacks.

An algorithm is presented for leader-following synchronization of a multi-agent system composed of linear agents with time delay. The presence of different delays in various agents can cause a synchronization error that does not converge to zero. However, the norm of this error can be bounded and this boundary is presented. The proof of the main results is formulated by means of linear matrix inequalities, and the size of this problem is independent of the number of agents. Results are illustrated through examples, highlighting the fact that the steady error is caused by heterogeneous delays and demonstrating the capability of the proposed algorithm to achieve synchronization up to a certain error.

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