Stability of Linear Volterra-Stieltjes Differential Equations
SIAM Journal on Control and Optimization
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We first introduce the notion of positive linear Volterra integrodifferential equations. Then we give some characterizations of these positive equations. An explicit criterion and a Perron-Frobenius-type theorem for positive linear Volterra integrodifferential equations are given. Then we offer a new criterion for uniformly asymptotic stability of positive equations. Finally, we study stability radii of positive linear Volterra integrodifferential equations. It is proved that complex, real, and positive stability radii of positive linear Volterra equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae. To the best of our knowledge, most of the results of this paper are new.