Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A Liapunov functional for linear Volterra integro-differential equations

Authors: D. L. Abrahamson and E. F. Infante
Journal: Quart. Appl. Math. 41 (1983), 35-44
MSC: Primary 45J05; Secondary 34K20
DOI: https://doi.org/10.1090/qam/700659
MathSciNet review: 700659
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Abstract: Liapunov functionals of quadratic form have been used extensively for the study of the stability properties of linear ordinary, functional and partial differential equations. In this paper, a quadratic functional $ V$ is constructed for the linear Volterra integrodifferential equation

$\displaystyle \dot x\left( t \right) = Ax\left( t \right) + \int_0^T {B\left( {... ...\ge {t_0}, \\ x\left( t \right) = f\left( t \right), \qquad 0 \le t \le {t_0}} $

. This functional, and its derivative $ \dot V$, is more general than previously constructed ones and still retains desirable computational qualities; moreover, it represents a natural generalization of the Liapunov function for ordinary differential equations. The method of construction used suggests functionals which are useful for more general equations.

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DOI: https://doi.org/10.1090/qam/700659
Article copyright: © Copyright 1983 American Mathematical Society

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