Uniform attractors of discontinuous semidynamical systems

• Autores: E. M. Bonotto, J.C.M. Ferreira
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 65, Fasc. 1, 2014, págs. 47-59
• Idioma: inglés
• DOI: 10.1007/s13348-012-0078-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • In the present paper, we define the concept of uniform attractor for semidynamical systems subject to variable impulses. We characterize the region of uniform attraction for compact sets and we show an asymptotic stability result for impulsive systems. Also, we present a result of uniform attractor by using Lyapunov functionals. We finish the paper by presenting an application for an impulsive nonlinear autonomous system.

• Referencias bibliográficas
  • Ambrosino, R., Calabrese, F., Cosentino, C., De Tommasi, G.: Sufficient conditions for finite-time stability of impulsive dynamical systems....
  • Barreira, L., Valls, C.: Lyapunov regularity of impulsive differential equations. J. Differ. Equ. 249(7), 1596–1619 (2010)
  • Bhatia, N.P., Hajek, O.: Local Semi-Dynamical Systems. Springer, Berlin (1969)
  • Bonotto, E.M., Federson, M.: Topological conjugation and asymptotic stability in impulsive semidynamical systems. J. Math. Anal. Appl. 326,...
  • Bonotto, E.M.: Flows of characteristic in impulsive semidynamical systems. J. Math. Anal. Appl. 332(1), 81–96 (2007)
  • Bonotto, E.M., Grulha Jr, N.G.: Lyapunov stability of closed sets in impulsive semidynamical systems. Electron. J. Differ. Equ. 78, 1–18 (2010)
  • Bonotto, E.M., Demuner, D.P.: Autonomous dissipative semidynamical systems with impulses. Topol. Methods Nonlinear Anal. (accepted)
  • Bouchard, B., Dang, N.-M., Lehalle, C.-A.: Optimal control of trading algorithms: a general impulse control approach. SIAM J. Finan. Math....
  • Cardinali, T., Servadei, R.: Periodic solutions of nonlinear impulsive differential inclusions with constraints. Proc. Am. Math. Soc. 132,...
  • Chu, J., Nieto, J.J.: Impulsive periodic solutions of first-order singular differential equations. Bull. Lond. Math. Soc. 40, 143–150 (2008)
  • Ciesielski, K.: On semicontinuity in impulsive dynamical systems. Bull. Polish Acad. Sci. Math. 52, 71–80 (2004)
  • Ciesielski, K.: On stability in impulsive dynamical systems. Bull. Polish Acad. Sci. Math. 52, 81–91 (2004)
  • Cortés, J.: Discontinuous dynamical systems: a tutorial on solutions, nonsmooth analysis, and stability. IEEE Control Syst. Mag. 28(3), 36–73...
  • Davis, M.H.A., Guo, X., Guoliang, W.: Impulse control of multidimensional jump diffusions. SIAM J. Control Optim. 48, 5276–5293 (2010)
  • Haddad, W.M., Hui, Q.: Energy dissipating hybrid control for impulsive dynamical systems. Nonlinear Anal. 69, 3232–3248 (2008)
  • Kaul, S.K.: On impulsive semidynamical systems. J. Math. Anal. Appl. 150(1), 120–128 (1990)