Poly-quadratic stability and global chaos synchronization of discrete time hybrid systems

This paper considers global chaos synchronization as an observer design problem. Chaos generators are ascribed the form of piecewise linear maps, a particular class of discrete time hybrid systems. Sufficient conditions of global synchronization are formulated using a poly-quadratic stability concept. Such a concept is based on the use of parameter-dependent Lyapunov functions to check stability and leads to a reduction of the restricitions relative to conditions involving a unique Lyapunov function.