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Chaos. 2016 Aug;26(8):084301. doi: 10.1063/1.4958713.

Stability and delay sensitivity of neutral fractional-delay systems.

Author information

1
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
2
Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023, China.

Abstract

This paper generalizes the stability test method via integral estimation for integer-order neutral time-delay systems to neutral fractional-delay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractional-delay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractional-delay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.

PMID:
27586618
DOI:
10.1063/1.4958713

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