论文标题
连续时间线性时间不变系统的稳定性分析
Stability Analysis of Continuous-Time Linear Time-Invariant Systems
论文作者
论文摘要
本文重点介绍了稳定性分析的数学方法，这是动态系统设计的关键步骤。提出了三种方法，即绝对可以集成的脉冲响应，傅立叶积分和拉普拉斯变换。拉普拉斯（Laplace）的优越性比其他方法的优势变得清晰，其原因包括以下几个原因：1）它允许分析稳定的系统以及不稳定的系统。 2）它不仅决定了绝对稳定性（是/否答案），而且还阐明了相对稳定性（系统的稳定性/不稳定），从而允许具有良好稳定性的设计。 3）其代数和卷积属性显着简化了分析中涉及的数学操纵，尤其是在处理由几个简单的系统组成的复杂系统时。对陌生读者进行了简要介绍系统主题的介绍。此外，提出了适当的物理概念和示例，以更好地清晰。
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and Laplace transform. The superiority of Laplace transform over the other methods becomes clear for several reasons that include the following: 1) It allows for the analysis of the stable, as well as, the unstable systems. 2) It not only determines absolute stability (a yes/no answer), but also shines light on the relative stability (how stable/unstable the system is), allowing for a design with a good degree of stability. 3) Its algebraic and convolution properties significantly simplify the mathematical manipulations involved in the analysis, especially when tackling a complex system composed of several simpler ones. A brief relevant introduction to the subject of systems is presented for the unfamiliar reader. Additionally, appropriate physical concepts and examples are presented for better clarity.
