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In this paper, we extend the eigenvalue method of the algebraic Riccatiequation to the differential Riccati equation (DRE) in contraction analysis.One of the main results is showing that solutions to the DRE can be expressedas functions of nonlinear eigenvectors of the differential Hamiltonian matrix.Moreover, under an assumption for the differential Hamiltonian matrix, realsymmetricity, regularity, and positive semidefiniteness of solutions arecharacterized by nonlinear eigenvalues and eigenvectors.

Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis