TY - JOUR

T1 - Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

AU - Reitmann, Volker

N1 - Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

AB - Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

KW - Absolute instability

KW - Frequency-domain method

KW - Infinite dimensional Volterra integral equation

KW - Realization theory

UR - http://www.scopus.com/inward/record.url?scp=79959301210&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79959301210

VL - 136

SP - 185

EP - 194

JO - Mathematica Bohemica

JF - Mathematica Bohemica

SN - 0862-7959

IS - 2

ER -