Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 45, Issue 3, Pages 572-575Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/9.847747
Keywords
Razumikhin theorem; stability; time delay systems
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In studying the stability of time delay systems, many published results use a transformation to transform a system with single time delay to a system with distributed delay In this article, the inherent limitations of such approaches are studied. Specifically, it is shown that such a transformation incurs additional dynamics that can be characterized by appropriate additional eigenvalues. The critical delay values when such additional eigenvalues cross the imaginary axis can be explicitly calculated. If the smallest of such delays is less than the stability delay limit of the original system, then any stability criteria obtained using such transformation will be conservative. Some examples are also included.
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