Send to

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

Stability and delay sensitivity of neutral fractional-delay systems.

Author information

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


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.


Supplemental Content

Full text links

Icon for American Institute of Physics
Loading ...
Support Center