Exponential asymptotic stability for linear volterra equations
Appleby, John A.D. (2000) Exponential asymptotic stability for linear volterra equations. Mathematical Proceedings of the Royal Irish Academy . pp. 1-7. ISSN 1393-7197
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This note studies the exponential asymptotic stability of the zero solution of the
linear Volterra equation
x˙ (t) = Ax(t) + t
K(t − s)x(s) ds
by extending results in the paper of Murakami “Exponential Asymptotic Stability
for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991.
In particular, when K isi ntegrable and has entries which do not change sign, and
the equation has a uniformly asymptotically stable solution, exponential asymptotic
stability can be identified by an exponential decay condition on the entries of K.
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