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Stability and delay sensitivity of neutral fractional-delay systems
Qi Xu1, Min Shi2, Zaihua Wang1
1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
Chaos (Woodbury, N.Y.)
|September 3, 2016
Summary
This study extends stability testing for neutral fractional-delay systems using integral estimation. It simplifies stability analysis by approximating unstable roots, revealing high sensitivity to time delays.
Area of Science:
- Control Theory
- Systems Engineering
- Applied Mathematics
Background:
- Stability analysis is crucial for time-delay systems.
- Existing methods for integer-order systems are limited.
- Fractional-delay systems present unique stability challenges.
Purpose of the Study:
- Generalize integral estimation for stability testing to neutral fractional-delay systems.
- Develop algorithms for estimating integral upper limits.
- Investigate the sensitivity of system stability to time delays.
Main Methods:
- Extending integral estimation techniques for stability analysis.
- Calculating the number of unstable characteristic roots via definite integrals.
- Developing parameter-dependent and independent algorithms for integral limit estimation.
Main Results:
- A simplified stability test for fractional-delay systems using rough integral estimation.
- Demonstration of extreme stability sensitivity to time delay variations.
- Validation through illustrative examples.
Conclusions:
- The proposed integral estimation method offers a straightforward approach to assess stability in neutral fractional-delay systems.
- Understanding delay sensitivity is critical for designing robust fractional-delay systems.
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