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.

中文翻译：

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线性分布阶系统中稳定性边界的性质

摘要 本文主要研究线性分布阶系统（LDOS）中的有界输入有界输出（BIBO）稳定性边界的一些行为。寻找 LDOS 的权重函数变化与其 BIBO 稳定性边界变化之间的关联是本文的另一个目的。为了实现这些目标，第一步是确定极高频和低频的 BIBO 稳定性边界的切线。然后，确定保持稳定边界完整的权重函数的加法恒等式和乘法恒等式。此外，证明了将一组多项式形式的乘法因子乘以权函数将保证稳定区域的增量。为了验证呈现的结果，对几种不同 LDOS 的稳定性边界进行了比较。模拟结果与提取结果一致。