Fast Sampling and Stability of Nonlinear Sampled-Data Systems: Part 1. Existence Theorems

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Abstract
The objective of this paper is to investigate how the choice of sampling interval is related to the stability of a class of nonlinear sampled-data systems, and in particular how fast sampling may stabilize a sampled-data system when the underlying continuous system is known to be stable. In this, the first, part of the paper, two fast sampling theorems are derived for a class of nonlinear sampled-data systems and it is shown that, provided the underlying continuous system is stable, there exists a maximum sampling interval such that when the system is sampled below this interval it will remain stable. In Part 2 of the paper, a special class of nonlinear sampled-data systems is studied and an analytical relationship between sampling rates and the domains of attraction of the system is derived.

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