27th Conference of the International Linear Algebra Society (ILAS 2026)

On the stability criteria via finite Hankel matrices for regular matrix polynomials

May 19, 2026, 2:00 PM

25m

Goodwin Hall 145 (Virginia Tech)

Minisymposium Talk Matrix Inequalities, Matrix Equations, and Their Applications Matrix Inequalities, Matrix Equations, and Their Applications

Speaker

Dr Xuzhou Zhan (Beijing Normal University at Zhuhai)

Description

This talk focuses on several stability criteria via Markov parameters for regular matrix polynomials, which generalize the corresponding criteria constrained by the monic assumption. The testing framework employs two finite Hankel matrices, whose rectangular blocks are the submatrices of the Markov parameters redefined through a column-wise splitting and column reduction for matrix polynomials. Specifically, a Hurwitz stability criterion is characterized by the Hermitian positive definiteness of two finite Hankel matrices. Further, our stability criterion is derived in terms of the Hermitian nonnegative definiteness and nullity of these finite Hankel matrices.