论文标题
参数化的LTI系统的不稳定性保证金分析，并应用于抑制剂
Instability Margin Analysis for Parametrized LTI Systems with Application to Repressilator
论文作者
论文摘要
本文与动态扰动下的单输入单输出不稳定的线性时间流（LTI）系统进行了强大的不稳定性分析。标称系统本身可能会受到不确定性的静态增益的扰动，当非线性不确定系统围绕平衡点线性化时，情况就是这种情况。我们将强大的不稳定性半径定义为稳定标称系统的稳定线性扰动的最小$ H_ \ infty $ norm。有两个主要的理论结果：一个是在不受干扰的名义系统的部分表征上，可以准确地计算出可靠的不稳定性半径，而另一个是一种数值可牵引的过程，用于计算由扰动参数参数化的名义性系统的确切可靠不稳定系统。结果应用于合成生物学中的抑制剂，在全球意义上，独特平衡的双曲不稳定性保证了振荡现象的持久性，并且我们的线性鲁棒不稳定性分析的有效性得到了数值模拟的确认。
This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the uncertainty, which would be the case when a nonlinear uncertain system is linearized around an equilibrium point. We define the robust instability radius as the smallest $H_\infty$ norm of the stable linear perturbation that stabilizes the nominal system. There are two main theoretical results: one is on a partial characterization of unperturbed nominal systems for which the robust instability radius can be calculated exactly, and the other is a numerically tractable procedure for calculating the exact robust instability radius for nominal systems parametrized by a perturbation parameter. The results are applied to the repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness of our linear robust instability analysis is confirmed by numerical simulations.
