Instability margin analysis for parametrized LTI systems with application to repressilator
Instability margin analysis for parametrized LTI systems with application to repressilator
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应用于抑制器的参数化 LTI 系统的不稳定裕度分析
DOI：
10.1016/j.automatica.2021.110047
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Yutaka Hori
中科院分区：
文献类型：
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作者：
S. Hara;T. Iwasaki;Yutaka Hori
研究了单输入单输出不稳定线性定常系统在动态扰动下的鲁棒不稳定性分析。标称系统本身可能受到不确定性的静态增益的扰动，这将是当非线性不确定系统在平衡点附近线性化时的情况。我们将鲁棒不稳定半径定义为使标称系统稳定的稳定线性扰动的最小H∞范数。有两个主要的理论结果：一个是在未扰动标称系统的鲁棒不稳定半径可以精确计算的部分特征，另一个是一个数值上易于处理的程序计算的精确鲁棒不稳定半径的标称系统参数化的扰动参数。结果被应用到represilator在合成生物学，双曲型不稳定的一个独特的平衡保证了持续的振荡现象在全球范围内的意义，我们的线性鲁棒不稳定性分析的有效性被证实的数值模拟。
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∞ 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.