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

Satoru Murakami; Pham Ngoc

Open Mathematics (2010)

  • Volume: 8, Issue: 5, page 966-984
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Satoru Murakami, and Pham Ngoc. "On stability and robust stability of positive linear Volterra equations in Banach lattices." Open Mathematics 8.5 (2010): 966-984. <http://eudml.org/doc/269541>.

@article{SatoruMurakami2010,
abstract = {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.},
author = {Satoru Murakami, Pham Ngoc},
journal = {Open Mathematics},
keywords = {Banach lattice; Volterra integro-differential equation; Positive system; Stability; Robust stability; positive system; stability; robust stability; positive co-semigroups; asymptotic stability},
language = {eng},
number = {5},
pages = {966-984},
title = {On stability and robust stability of positive linear Volterra equations in Banach lattices},
url = {http://eudml.org/doc/269541},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Satoru Murakami
AU - Pham Ngoc
TI - On stability and robust stability of positive linear Volterra equations in Banach lattices
JO - Open Mathematics
PY - 2010
VL - 8
IS - 5
SP - 966
EP - 984
AB - 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.
LA - eng
KW - Banach lattice; Volterra integro-differential equation; Positive system; Stability; Robust stability; positive system; stability; robust stability; positive co-semigroups; asymptotic stability
UR - http://eudml.org/doc/269541
ER -

References

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  12. [12] Ngoc P.H.A., Naito T., Shin J.S., Murakami S., On stability and robust stability of positive linear Volterra equations, SIAM J. Control Optim., 2008, 47(2), 975–996 http://dx.doi.org/10.1137/070679740 Zbl1206.45009
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