Stability of positive linear Volterra integro-differential systems with delays

Ilchmann, Achim GND; Ngoc, Pham Huu Anh

We study positive linear Volterra integro-differential systems with infinitely many delays. Positivity is characterized in terms of the system entries. A generalized version of the Perron-Frobenius Theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L1-stability and exponential asymptotic stability. Also the concept of stability radii, determining the maximal robustness with respect to additive perturbations to L1-stable system, is introduced and it is shown that the complex, real and positive stability radii coincide and can be computed by an explicit formula.

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Ilchmann, Achim / Ngoc, Pham Huu Anh: Stability of positive linear Volterra integro-differential systems with delays. 2008.

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