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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