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Interconnected discrete-time systems with incommensurate clock frequencies

This paper proposes a model that recurrently determines the switching patterns of two interconnected discrete-time systems with small differences in the clock frequencies. It is based on a time-variant or switched state-space representation of both systems. The method uses a continued fraction representation of the sampling period ratio of the two systems. Based on this result a stability test is derived, which can be made arbitrarily close to being a necessary and sufficient stability condition. This problem frequently occurs in networked systems where network nodes cannot be exactly synchronized with each other.