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首页> 外文期刊>Automatic Control, IEEE Transactions on >Colored Stability Crossing Sets for SISO Delay Systems
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Colored Stability Crossing Sets for SISO Delay Systems

机译：SISO延迟系统的彩色稳定性交叉集

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This paper considers the stability of a single-input single-output (SISO) system with an input/output (I/O) delay, called SISO delay system hereafter. We first derive an algebraic criterion to solve the complete stability w.r.t. the delay τ. Next, the stability analysis is extended to the case with additional free (plant and/or controller) parameters, denoted by a vector X. By adopting a mathematical tool for polynomial algebra, the discrimination system, the complete classification of the critical imaginary roots (CIRs) in the whole X-τ parameter space may be obtained. Furthermore, with the above results, we present the stability crossing sets (SCSs) in a new form, called the colored SCSs. For each point on the SCS the asymptotic behavior information of the corresponding CIR can be coded by a certain color (red, green, or yellow). Hence, the stability in the X-τ space can be analyzed easily and intuitively. Moreover, the geometry of the SCSs can be investigated from a new perspective, which will help not only to better understand the stability of the SISO delay system but also to considerably simplify the procedure for generating the colored SCSs.
机译：本文考虑具有输入/输出（I / O）延迟的单输入单输出（SISO）系统的稳定性，此后称为SISO延迟系统。我们首先导出一个代数准则以解决w.r.t的完全稳定性。延迟τ。接下来，将稳定性分析扩展到带有附加自由（植物和/或控制器）参数（用矢量X表示）的情况。可以获得整个X-τ参数空间中的CIR。此外，根据以上结果，我们以一种称为彩色SCS的新形式展示了稳定性交叉集（SCS）。对于SCS上的每个点，可以使用某种颜色（红色，绿色或黄色）对相应CIR的渐近行为信息进行编码。因此，可以轻松直观地分析X-τ空间中的稳定性。此外，可以从新的角度研究SCS的几何形状，这不仅有助于更好地了解SISO延迟系统的稳定性，而且可以大大简化生成彩色SCS的过程。

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