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Stability and robust stability of positive Volterra systems
Author(s) -
Ilchmann Achim,
Ngoc Pham Huu Anh
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1712
Subject(s) - exponential stability , mathematics , stability (learning theory) , volterra equations , robustness (evolution) , control theory (sociology) , stability theorem , mathematical analysis , nonlinear system , computer science , physics , biochemistry , chemistry , control (management) , quantum mechanics , machine learning , artificial intelligence , cauchy distribution , gene
SUMMARY 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 L 1 ‐stability and exponential asymptotic stability. Also, the concept of stability radii, determining the maximal robustness with respect to additive perturbations to L 1 ‐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. Copyright © 2011 John Wiley & Sons, Ltd.
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