EMOSC 25: Energy-based modeling, simulation, and control of dynamical systems - Workshop in honor of Volker Mehrmann’s 70th birthday

Invariant subspace perturbations of Hamiltonian matrices with defective imaginary eigenvalues

27 May 2025, 16:30

30m

Faculty of Mathematics

Talk Talks

Speaker

Hongguo Xu (University of Kansas)

Description

We show how invariant subspaces will change when a defective matrix
is perturbed. We focus on the case when an invariant subspace corresponding to
the same size Jordan blocks of a single eigenvalue is perturbed.
The perturbations are characterized in terms of fractional orders.
As an application, we study a class of Hamiltonian matrices
that are related to Riccati inequalities. We show how the purely imaginary eigenvalues
and their invariant subspaces are perturbed under certain structured perturbations.