关于逼近最近 Ω-稳定矩阵
On approximating the nearest Ω-stable matrix
AI总结：
本文研究最近 Ω-稳定矩阵逼近问题，利用耗散哈密顿矩阵和线性矩阵不等式将其重构为凸可行集问题，并用块坐标下降法求解。
摘要：
本文研究用特征值位于复平面特定区域 Ω 内的矩阵来逼近给定矩阵的问题。更确切地说，我们考虑三类区域及其交集：圆锥扇区、垂直条带和圆盘。我们将此问题称为最近 Ω-稳定矩阵问题。它包含了连续和离散时间线性时不变系统的稳定矩阵作为特例。为实现该目标，我们使用耗散哈密顿矩阵和线性矩阵不等式对该问题进行参数化。这使得问题被重新表述为具有凸可行集的形式。通过对该重构问题应用块坐标下降法，我们能够计算出逼近问题的解，并通过若干示例进行了说明。
英文摘要：
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω, within the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips and disks. We refer to this problem as the nearest Ω-stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time-invariant systems. In order to achieve this goal, we parametrize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
