Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis
Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis
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用于收缩分析的微分 Riccati 方程的非线性特征值方法
DOI：
10.1109/tac.2017.2655443
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发表时间：
2017
影响因子：
6.8
通讯作者：
and Toshiyuki Ohtsuka
中科院分区：
文献类型：
--
作者：
Yu Kawano;and Toshiyuki Ohtsuka
本文将代数Riccati方程的特征值法推广到微分Riccati方程（DRE）的收缩分析中。其中一个主要的结果是表明DRE的解可以表示为微分哈密顿矩阵的非线性特征向量的函数。此外，在微分哈密顿矩阵的假设下，解的实对称性、正则性和正半正定性被非线性特征值和特征向量所表征。
In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear eigenvectors of the differential Hamiltonian matrix. Moreover, under an assumption for the differential Hamiltonian matrix, real symmetry, regularity, and positive semidefiniteness of solutions are characterized by nonlinear eigenvalues and eigenvectors.