Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations
Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations
复制标题
结构保持扰动下具有耗散的线性哈密顿系统的稳定性半径
DOI：
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发表时间：
2016
影响因子：
1.5
通讯作者：
Punit Sharma
中科院分区：
文献类型：
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作者：
C. Mehl;V. Mehrmann;Punit Sharma
耗散哈密顿 (DH) 系统是基于能量的动力系统建模中的一个重要概念。 DH 公式的主要优点之一是系统属性以代数方式编码。例如，DH系统的代数结构保证了系统自动稳定。本文讨论了当线性常系数 DH 系统位于渐近稳定区域的边界时，即当它具有纯虚数特征值时，或者它必须受到多少扰动才能位于该边界上的问题。对于非结构化系统，这种到不稳定的距离（稳定半径）是很好理解的。在本文中，确定了结构保持扰动下该距离的显式公式。还表明（通过数值例子），在结构保持扰动下，DH 系统的渐近稳定性比一般扰动下更加鲁棒，因为当结构保持时，到不稳定的距离可能会大得多。
Dissipative Hamiltonian (DH) systems are an important concept in energy based modeling of dynamical systems. One of the major advantages of the DH formulation is that system properties are encoded in an algebraic way. For instance, the algebraic structure of DH systems guarantees that the system is automatically stable. In this paper the question is discussed when a linear constant coefficient DH system is on the boundary of the region of asymptotic stability, i.e., when it has purely imaginary eigenvalues, or how much it has to be perturbed to be on this boundary. For unstructured systems this distance to instability (stability radius) is well understood. In this paper, explicit formulas for this distance under structure-preserving perturbations are determined. It is also shown (via numerical examples) that under structure-preserving perturbations the asymptotical stability of a DH system is much more robust than under general perturbations, since the distance to instability can be much larger when struc...