Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques. This book also: Presents novel concepts and methods for dynamical system synchronization Extends beyond the Lyapunov theory for dynamical system synchronization Introduces companion and synchronization of discrete dynamical systemsIncludes local singularity theory for discontinuous dynamical systems Covers the invariant domains of synchronizationFeatures more than 75 illustrationsDynamical System Synchronization is an ideal book for those interested in better understanding new concepts and methodology for dynamical system synchronization, local singularity theory for discontinuous dynamical systems, distinct dynamical system synchronization, and invariant domains of synchronization.