ABSTRACT
This chapter presents chaotic systems admitting a polytopic description and some background concerning the notion of poly-quadratic stability. It deals with the message-free and the message-embedded chaos synchronization problem. A systematic procedure is stated for the design of the polytopic observers which must achieve global synchronization in the message-free context and additionally the recovering of the masked information in the message-embedded context. The interest in chaos synchronization has increased in the last decade since the pioneering works by L. M. Pecora and T. L. Carroll. One of the well-known practical interests of chaos synchronization lies in the potential applications in communications, and more specifically in the possibilities of encoding or masking messages by suitable embedding. Poly-quadratic stability has been introduced earlier to state necessary and sufficient conditions of existence of Parameter Dependent Liapunov Functions in the context of linear parameter varying systems.
