Abstract
A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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Anderson, R.F.V. The relative variance criterion for stability of delay systems. J Dyn Diff Equat 5, 105–128 (1993). https://doi.org/10.1007/BF01063737
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DOI: https://doi.org/10.1007/BF01063737