Poly-quadratic stability and global chaos synchronization of discrete time hybrid systems
This paper deals with the chaos synchronization of some type of discrete hybrid systems with applications to the reproducibility of chaotic behaviours through synchronization to problems of secure communications. The systems under consideration are composed of a receiver and a transmitter whose states are defined by finite \(n\)-dimensional vectors \( X_k^r \) and \( X_k^t\), \( k=1,2, \ldots \) respectively and the reconstruction is based in a gain matrix computation of the observer. The main problem is to determine conditions under which the state vector of the receiver converges towards that of the transmitter for arbitrary initial conditions. In this setting, assuming that both transmitters and receivers are described by piecewise linear maps the authors provide sufficient conditions in terms of linear matrix inequalities of global stability involving the use of Lyapunov type functions. Finally, a simple example is presented to illustrate the behaviour of the theory for several choices of output matrices.
scientific article; zbMATH DE number 1758397