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Stability test of fractional-delay systems via integration

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Abstract

This paper focuses on the stability testing of fractional-delay systems. It begins with a brief introduction of a recently reported algorithm, a detailed demonstration of a failure in applications of the algorithm and the key points behind the failure. Then, it presents a criterion via integration, in terms of the characteristic function of the fractional-delay system directly, for testing whether the characteristic function has roots with negative real parts only or not. As two applications of the proposed criterion, an algorithm for calculating the rightmost characteristic root and an algorithm for determining the stability switches, are proposed. The illustrative examples show that the algorithms work effectively in the stability testing of fractional-delay systems.

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Authors and Affiliations

  1. Institute of Science, PLA University of Science and Technology, Nanjing, 211101, China

    ZaiHua Wang & MaoLin Du

  2. State Key Laboratory of Mechauics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    ZaiHua Wang & Min Shi

Authors
  1. ZaiHua Wang
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  2. MaoLin Du
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  3. Min Shi
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Correspondence to ZaiHua Wang.

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Wang, Z., Du, M. & Shi, M. Stability test of fractional-delay systems via integration. Sci. China Phys. Mech. Astron. 54, 1839 (2011). https://doi.org/10.1007/s11433-011-4447-1

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  • DOI: https://doi.org/10.1007/s11433-011-4447-1

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