Matrix analysis
One-parameter semigroups of postive operators
One-parameter semigroups of postive operators
Volterra Integral and Differential Equations: SECOND EDITION (Mathematics in Science and Engineering)
On Stability and Robust Stability of Positive Linear Volterra Equations
SIAM Journal on Control and Optimization
On Positivity and Stability of Linear Volterra Systems with Delay
SIAM Journal on Control and Optimization
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Linear Volterra-Stieltjes differential equations are considered. We give a sufficient condition which ensures that the uniform asymptotic stability and the exponential asymptotic stability of linear Volterra-Stieltjes differential equations coincide. In particular, this yields necessary and sufficient conditions for the exponential asymptotic stability of linear Volterra-Stieltjes differential equations whose kernels are monotone. Then the class of positive linear Volterra-Stieltjes differential equations is studied in detail and simple criteria for the exponential asymptotic stability of positive equations are presented. Furthermore, some sufficient conditions for the exponential asymptotic stability of positive equations subjected to structured perturbations and affine perturbations are provided. Finally, by applying obtained results to linear Volterra integro-differential equations with infinite delay, we get explicit criteria for the exponential asymptotic stability of positive equations with delay. To the best of our knowledge, most of the obtained results of this paper are new.