Contraction analysis of Volterra integral equations via realization theory and frequency-domain methods

Abstract

<p style='text-indent:20px;'>Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the contraction analysis of a class of nonlinear Volterra integral equations in some Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in some weighted Sobolev space which has the same stability properties as the Volterra equation.</p>