A new theorem to synchronization of unified chaotic systems via adaptive control

Chaos synchronization has been applied in secure communication, chemical reaction, biological systems, and information processing. A new theorem to synchronization of unified chaotic systems via adaptive control is proposed. The consutructive theorem provides the design scheme for adaptive controller such that a respond system can synchronize with respect to an uncertain drive system. One example for discontinuous chaotic system is proposed to illustrate the effectiveness and feasibility.