论文标题
关于BIBO稳定性的注释
A Note on BIBO Stability
论文作者
论文摘要
工程教科书中发现的连续时间卷积系统的BIBO稳定性的陈述通常太模糊（由于缺乏假设）或数学不正确。更令人不安的是，他们通常排除身份操作员。本说明的目的是在提出一些修复程序时澄清问题。特别是，我们表明，当$ l_ \ infty $ -sense中，当且仅当其脉冲响应中包含在界限radon测量的空间中时，线性换档系统在$ l_ \ infty $ - sense中是bibo stable，这是$ l_1（\ mathbb {r}）的超集，这是$ l_1（\ mathbb {r}）$（lebesgue（lebesgue）$（lebesgue绝对可集成的函数）。当我们将这种表征的范围限制为脉冲响应是可衡量的函数的卷积运算符时，我们恢复了经典陈述。
The statements on the BIBO stability of continuous-time convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identity operator. The purpose of this note is to clarify the issue while presenting some fixes. In particular, we show that a linear shift-invariant system is BIBO-stable in the $L_\infty$-sense if and only if its impulse response is included in the space of bounded Radon measures, which is a superset of $L_1(\mathbb{R})$ (Lebesgue's space of absolutely integrable functions). As we restrict the scope of this characterization to the convolution operators whose impulse response is a measurable function, we recover the classical statement.
