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

Abstract

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.

New Challenges in Dynamical Systems: The Networked Case

“…For details on modeling, stability and performance of these systems see, (Lorand and Bauer, 2005;Lorand and Bauer, 2006a;Lorand and Bauer, 2006b). …”

Identification of clock synchronization errors: A behavioral approach

“…The analysis in this paper will also require the extended observability matrix for discrete linear time invariant systems described by (1), that is,…”

Stability and robustness of systems with synchronization errors

“…It was shown in [5] that most synchronous systems totally change their response if operated asynchronously. Even stability is often lost [5]- [6] and there is generally no stability robustness with respect M. Przedwojski to synchronization errors, with the exception of work in [7], [8] that are very limited in terms of application to practically relevant cases.…”

“…In general, two types of asynchronous behavior can arise [5], where in one all subsystems are driven by the same clock but switching times are different between subsystems, and in the other individual subsystems are driven by the same clocks with different frequencies. In the first case, switching patterns are simple but in the second case are very hard to specify [9].…”

“…Previous work has addressed system models and the resulting stability behavior [5]- [9], but no attempt has been made to stabilize the overall asynchronous system network. In this paper we give major new results in this area by showing how to stabilize an asynchronous network of systems through state feedback.…”