On stability and robust stability of positive linear Volterra equations in Banach lattices

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stabilit...

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Veröffentlicht in:	Central European journal of mathematics 2010-10, Vol.8 (5), p.966-984
Hauptverfasser:	Murakami, Satoru, Ngoc, Pham Huu Anh
Format:	Artikel
Sprache:	eng
Schlagworte:	34A30 34K20 93D09 Algebra Banach lattice Differential equations Geometry Lattices (mathematics) Lie Groups Mathematical analysis Mathematics Mathematics and Statistics Number Theory Perturbation Positive system Probability Theory and Stochastic Processes Research Article Robust stability Robustness Stability Topological Groups Volterra integral equations Volterra integro-differential equation
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Zusammenfassung:	We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
ISSN:	1895-1074 1644-3616 2391-5455
DOI:	10.2478/s11533-010-0061-0