Parameter dependent Lyapunov function for global chaos synchronization of discrete time hybrid systems

Consideration of global chaos synchronization as an observer design problem is addressed. Chaos generators gets the form of piecewise linear maps, a particular class of discrete time hybrid systems. This enables to derive sufficient conditions of global synchronization from robust control theory results. The use of a parameter dependant Lyapunov function of which parametrization is related to each local linear dynamics of the map leads to a reduction of the conservatism of the conditions involving a unique Lyapunov function.