Properties of the stability boundary in linear distributed-order systems

Ehsan Majma and Mohammad Saleh Tavazoei

International Journal of Systems Science, 2020, vol. 51, issue 10, 1733-1743

Abstract: This paper mainly focuses on some behaviours of the bounded input-bounded output (BIBO) stability boundary in the linear distributed-order system (LDOS). Finding an association between changes of weight functions of LDOS and variation of its BIBO stability boundary is the other aim of this paper. To achieve these goals, the tangential lines of the BIBO stability boundary for the extremely high and low frequencies are founded in the first step. Then, the additive identity and the multiplicative identity for the weight function maintaining the stability boundary intact are determined. In addition, it is proved that multiplying a set of multiplication factors in the form of polynomials to the weight functions would guarantee the increment of the stability region. To validate the presented results, comparisons among the stability boundary of several different LDOS are performed. Simulation outcomes are in agreement with the extracted results.

Date: 2020
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DOI: 10.1080/00207721.2020.1773959

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