Stability radius of linear parameter-varying systems and applications
Stability radius of linear parameter-varying systems and applications
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DOI：
10.1109/cdc.2006.377509
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
P. H. A. Ngoc;Toshiki Naito
中科院分区：
文献类型：
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作者：
P. H. A. Ngoc;Toshiki Naito
本文给出了正线性系统稳定半径计算问题的一种统一方法。首先，研究了线性定常变参微分系统的稳定性半径。给出了多摄动下复稳定半径的计算公式。然后，在系统矩阵为正的假设下，证明了系统在多重扰动下的复稳定半径、实稳定半径和正稳定半径重合，并用一个简单的公式计算了它们。作为应用，我们研究了线性时不变时滞微分系统的（强）稳定半径的计算问题和多摄动下线性正泛函微分方程的稳定半径的计算问题。证明了一类正线性时滞微分系统在多重扰动下的稳定半径等于强稳定半径。其次，我们证明了一个正线性泛函微分方程在多重扰动下的稳定性半径等于相应的线性定常参变微分系统的稳定性半径。特别是，我们得到了Ngoc等人（2005）给出的这些稳定半径的一些显式公式。由于篇幅的关系，本文将曝光量控制在最小
In this paper, we present an unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system matrices, we prove that the complex, real and positive stability radius of the system under multi perturbations coincide and they are computed via a simple formula. As applications, we consider problems of computing of (strong) stability radii of linear time-invariant time-delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations. We show that for a class of positive linear time-delay differential systems, the stability radii of the system under multi perturbations are equal to the strong stability radii. Next, we prove that the stability radii of a positive linear functional differential equation under multi perturbations are equal to those of the associated linear time-invariant parameter-varying differential system. In particular, we get back some explicit formulas for these stability radii which were given by Ngoc et al., (2005). For sake of space, exposure is kept to minimum in this paper