Designing self-synchronizing switched linear systems: An application to communications

This paper addresses the problem of self-synchronizing dynamical systems in a so-called master-slave configuration. The study is motivated by potential cryptographic applications. It is shown that the notion of flatness is central for guaranteeing a finite-time self-synchronization and that the concept of transmission zero plays also an important role. Next, the finite-time synchronization is relaxed to give rise to a so-called statistical self-synchronization, a mode of operation which makes sense in classical cryptography which operates over finite fields. The fact that switched linear systems are of great interest in this context is motivated.