Stability of positive linear Volterra integro-differential systems with delays

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.

Zitieren

Zitierform:
Zitierform konnte nicht geladen werden.

Rechte

Nutzung und Vervielfältigung:
Alle Rechte vorbehalten