The stability of linear periodic Hamiltonian systems on time scales

Zafer A.

APPLIED MATHEMATICS LETTERS, vol.26, no.3, pp.330-336, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1016/j.aml.2012.09.014
  • Journal Name: APPLIED MATHEMATICS LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.330-336
  • Keywords: Hamiltonian system, Time scale, Stability, Floquet multiplier, LYAPUNOV INEQUALITIES, DISCONJUGACY, CRITERIA
  • Middle East Technical University Affiliated: Yes

Abstract

In this work, we give a new stability criterion for planar periodic Hamiltonian systems, improving the results from the literature. The method is based on an application of the Floquet theory recently established in [J.J. DaCunha, J.M. Davis, A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems, J. Differential Equations 251 (2011) 2987-3027], and the use of a new definition for a generalized zero. The results obtained not only unify the related continuous and discrete ones but also provide sharper stability criteria for the discrete case. (C) 2012 Elsevier Ltd. All rights reserved.