TY - JOUR

T1 - Norm estimates for function Lyapunov equations and applications

AU - Gil, Michael

N1 - Publisher Copyright:
© 2018 The Franklin Institute

PY - 2018/7/1

Y1 - 2018/7/1

N2 - We consider the function Lyapunov equation f*(A)X+Xf(A)=C, where A and C are given matrices, f(z) is a function holomorphic on a neighborhood of the spectrum σ(A) of A. For a solution X of that equation, norm estimates are established. By these estimates we investigate perturbations of a matrix A whose spectrum satisfies the condition infℜσ(f(A))>0. In the case f(z)=zν with a positive integer ν we obtain conditions that provide localization of the spectrum of a perturbed matrix in a given angle.

AB - We consider the function Lyapunov equation f*(A)X+Xf(A)=C, where A and C are given matrices, f(z) is a function holomorphic on a neighborhood of the spectrum σ(A) of A. For a solution X of that equation, norm estimates are established. By these estimates we investigate perturbations of a matrix A whose spectrum satisfies the condition infℜσ(f(A))>0. In the case f(z)=zν with a positive integer ν we obtain conditions that provide localization of the spectrum of a perturbed matrix in a given angle.

UR - http://www.scopus.com/inward/record.url?scp=85046156408&partnerID=8YFLogxK

U2 - 10.1016/j.jfranklin.2018.04.005

DO - 10.1016/j.jfranklin.2018.04.005

M3 - Article

AN - SCOPUS:85046156408

VL - 355

SP - 4241

EP - 4247

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

SN - 0016-0032

IS - 10

ER -