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2010 | 8 | 5 | 966-984
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On stability and robust stability of positive linear Volterra equations in Banach lattices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
5
Strony
966-984
Opis fizyczny
Daty
wydano
2010-10-01
online
2010-09-28
Twórcy
autor
Bibliografia
  • [1] Engel K.-J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., 194, Springer, Berlin, 2000
  • [2] Gripenberg G., Londen L.O., Staffans O.J., Volterra Integral and Functional Equations, Encyclopedia Math. Appl., 34, Cambridge University Press, Cambridge, 1990
  • [3] Henríquez H. R., Periodic solutions of quasi-linear partial functional differential equations with unbounded delay, Funkcial. Ekvac., 1994, 37(2), 329–343
  • [4] Hille E., Phillips R.S., Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ., 31, AMS, Providence, 1957
  • [5] Hino Y., Murakami S., Stability properties of linear Volterra integrodifferential equations in a Banach space, Funkcial. Ekvac., 2005, 48(3), 367–392 http://dx.doi.org/10.1619/fesi.48.367
  • [6] Kantorovich L.V., Akilov G.P., Functional Analysis, Pergamon Press, 1982
  • [7] Meyer-Nieberg P., Banach Lattices, Universitext, Springer, Berlin, 1991
  • [8] Nagel R. (ed.), One-parameter Semigroups of Positive Operators, Lecture Notes in Math., 1184, Springer, Berlin, 1986
  • [9] Ngoc P.H.A., Son N.K., Stability radii of linear systems under multi-perturbations, Numer. Funct. Anal. Optim., 2004, 25(3–4), 221–238 http://dx.doi.org/10.1081/NFA-120039610
  • [10] Ngoc P.H.A., Son N.K., Stability radii of positive linear functional differential equations under multi-perturbations, SIAM J. Control Optim., 2005, 43(6), 2278–2295 http://dx.doi.org/10.1137/S0363012903434789
  • [11] Ngoc P.H.A., Minh N.V., Naito T., Stability radii of positive linear functional differential systems in Banach spaces, Int. J. Evol. Equ., 2007, 2(1), 75–97
  • [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
  • [13] Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Springer, New York, 1984
  • [14] Prüss J., Evolutionary Integral Equations and Applications, Monogr. Math., 87, Birkhäuser, Basel, 1993
  • [15] Schaefer H.H., Banach Lattices and Positive Operators, Grundlehren Math. Wiss., 215, Springer, Berlin, 1974
  • [16] Stewart H.B., Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc., 1980, 259(1), 299–310
  • [17] Zaanen A.C., Introduction to Operator Theory in Riesz Spaces, Springer, Berlin, 1997
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0061-0
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