Distributed discrete-time systems with synchronization errors: models and stability

The problem addressed in this brief originates from the use of nonidentical clocks in distributed systems, i.e., clocks with slightly different frequencies. At first, we introduce an event driven state space model for asynchronous system equations. Then, we derive necessary and sufficient conditions for stability and show that unlike in the case of synchronous operations, the slightest mismatch in clock frequencies can destabilize the system, even if the synchronously operating system has a large margin of stability. New light is shed on the importance of the degree of synchronization and its connection to stability.