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On stability and robust stability of positive linear Volterra equations in Banach lattices

Satoru Murakami, Pham Ngoc (2010)

Open Mathematics

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.

On stability of linear neutral differential equations with variable delays

Leonid Berezansky, Elena Braverman (2019)

Czechoslovak Mathematical Journal

We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x ˙ ( t ) - a ( t ) x ˙ ( g ( t ) ) + b ( t ) x ( h ( t ) ) = 0 , where | a ( t ) | < 1 , b ( t ) 0 , h ( t ) t , g ( t ) t , and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

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