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This paper addresses the problem of synchronization errors and their effects on feedback loops that are closed over communication networks. It is assumed that the feedback loop consists of two discrete-time systems, the clock frequency ratio of which has a special rational form, and is close to one. A Toeplitz matrix approach is taken to model the input/output relationship of the arising feedback systems. Based on this representation, the effect of synchronization errors on stability of the feedback systems is analyzed. It is shown that stability of the synchronized feedback loop can not guarantee stability of the loop in the presence of synchronization errors. Necessary and sufficient stability conditions are derived.

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.

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This paper models and analyzes the effect of multiple sub-systems that are driven by the same clock signal with active clock edges reaching subsystems at different time instants. This type of problem appears in high speed circuits and systems where the clock signal propagation delays differ significantly and the global system properties of the ideally synchronously switching system are changed. Fault detection and identification methods for this type of system are provided, by using a state-space approach to asynchronously switching systems.