Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

A SHORT REMARK ON CONTROL SYSTEMS

  • Chu, Hahng-Yun (Department of Mathematics, Chungnam National University) ;
  • Ku, Se-Hyun (Department of Mathematics, Chungnam University) ;
  • Yoo, Seung Ki (Department of Mathematics, Chungnam University)
  • Received : 2016.01.19
  • Accepted : 2016.02.05
  • Published : 2016.02.15
Download PDF
⟨ Previous Next ⟩

Abstract

Souza and Tozatti [7] introduce the notions of prolongations and prolongational limit sets on control systems. In this article, we prove the upper semicontinuity of first positive prolongations and first positive prolongational limit sets on control systems.

Keywords

References

  1. N. P. Bhatia and G. P. Szego, Stability Theory of Dynamical Systems, Die Grundlehren der mathematischen Wissenschaften, Band 161 Springer-Verlag, New York-Berlin 1970.
  2. E. M. Bonotto and M. Federson, Topological conjugation and asymptotic stability in impulsive semidynamical systems, J. Math. Anal. Appl. 326 (2007), no. 2, 869-881. https://doi.org/10.1016/j.jmaa.2006.03.042
  3. E. M. Bonotto and M. Federson, Limit sets and the Poincare-Bendixson theorem in impulsive semidynamical systems, J. Differential Equations 244 (2008), no. 9, 2334-2349. https://doi.org/10.1016/j.jde.2008.02.007
  4. E. M. Bonotto and M. Federson, Poisson stability for impulsive semidynamical systems, Nonlinear Anal. 71 (2009), no. 12, 6148-6156. https://doi.org/10.1016/j.na.2009.06.008
  5. F. Colonius and W. Kliemann, The Dynamics of Control, Birkhauser, Boston, 2000.
  6. S.-H. Ku and S. K. Yoo, Limit sets on control systems, submitted.
  7. J. A. Souza and Helio V. M. Tozatti, Prolongational limit sets of control systems, J. Differential Equations 254 (2013), no. 5, 2183-2195. https://doi.org/10.1016/j.jde.2012.11.020