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IMA Journal of Mathematical Control and Information 1990 7(1):1-11; doi:10.1093/imamci/7.1.1
© 1990 by Institute of Mathematics and its Applications
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Fast Sampling and Stability of Nonlinear Sampled-Data Systems: Part 1. Existence Theorems

D. H. OWENS, Y. ZHENG and S. A. BILLINGS

Department of Mathematics, University of Strathclyde 26 Richmond Street, Glasgow G1 1XH, Scotland, UK
Department of Control Engineering, University of Sheffield Mappin Street, Sheffield S1 3JD, UK

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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