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Pullback incremental attraction

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.
Wydawca
Rocznik
Tom
1
Opis fizyczny
Daty
otrzymano
2013-09-06
zaakceptowano
2013-11-11
online
2013-12-27
Twórcy
Bibliografia
  • [1] D. Angeli, A Lyapunov approach to the incremental stability properties, IEEE Trans. Automat. Control 47 (2002),410-421.
  • [2] T. Caraballo, M.J. Garrido Atienza and B. Schmalfuß, Existence of exponentially attracting stationary solutions fordelay evolution equations. Discrete Contin. Dyn. Syst. Ser. A 18 (2007), 271-293.
  • [3] T. Caraballo, P.E. Kloeden and B. Schmalfuß, Exponentially stable stationary solutions for stochastic evolutionequations and their perturbation. Appl. Math. Optim. 50 (2004), 183-207.
  • [4] C.M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971), 239-252.
  • [5] L. Grüne, P.E. Kloeden, S. Siegmund and F.R. Wirth, Lyapunov’s second method for nonautonomous differentialequations, Discrete Contin. Dyn. Syst. Ser. A 18 (2007), 375-403.
  • [6] P.E. Kloeden, Lyapunov functions for cocycle attractors in nonautonomous difference equations, Izvetsiya Akad NaukRep Moldovia Mathematika 26 (1998), 32-42.
  • [7] P.E. Kloeden, A Lyapunov function for pullback attractors of nonautonomous differential equations, Electron. J. Differ.Equ. Conf. 05 (2000), 91-102.
  • [8] P.E. Kloeden and T. Lorenz, Stochastic differential equations with nonlocal sample dependence, Stoch. Anal. Appl.28 (2010), 937-945.
  • [9] P.E. Kloeden and T. Lorenz, Mean-square random dynamical systems, J. Differential Equations 253 (2012), 1422-1438.
  • [10] P.E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Amer. Math. Soc., Providence, 2011.
  • [11] B.S. Rüffer, N. van de Wouw and M. Mueller, Convergent systems vs. incremental stability, Systems Control Lett.62 (2013), 277-285.
  • [12] E.D. Sontag, Comments on integral variants of ISS, Systems Control Lett. 34 (1998), 93-100.
  • [13] A.M. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge,1996.
  • [14] Fuke Wu and P.E. Kloeden, Mean-square random attractors of stochastic delay differential equations with randomdelay, Discrete Contin. Dyn. Syst. Ser. B 18, No.6, (2013), 1715-1734.
  • [15] T. Yoshizawa, Stability Theory by Lyapunov’s Second Method. Math. Soc Japan, Tokyo, 1966.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_msds-2013-0004
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