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

• Autorzy: Satoru Murakami , Pham Ngoc
• 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.

Słowa kluczowe

EN

Banach lattice; Volterra integro-differential equation; Positive system; Stability; Robust stability

Kategorie tematyczne

• 34K20: Stability theory
• 93D09: Robust stability
• 34A30: Linear equations and systems, general

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 5
• Strony: 966-984

Daty

wydano

2010-10-01

online

2010-09-28

Twórcy

autor

Satoru Murakami

• Okayama University of Science

autor

Pham Ngoc

• Vietnam National University-HCMC (VNU-HCM), International University

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

Identyfikatory

DOI

10.2478/s11533-010-0061-0