Riccati微分方程压缩分析的非线性Eigenvalue方法
Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis
摘要：
本文将压缩分析中代数Riccati方程的特征值方法推广到微分Riccati方程。主要结果之一是证明了DRE的解可以表示为微分Hamilton矩阵的非线性特征向量的函数。此外，在微分Hamilton矩阵的假设下，用非线性特征值和特征向量刻画了解的实收敛性、正则性和半正定性.
英文摘要：
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 symmetricity, regularity, and positive semidefiniteness of solutions are characterized by nonlinear eigenvalues and eigenvectors.
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