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  • Research Article
  • Open Access

On the estimation of upper bound for solutions of perturbed discrete Lyapunov equations

Journal of Inequalities and Applications20062006:58931

  • Received: 20 February 2006
  • Accepted: 12 June 2006
  • Published:


The estimation of the positive definite solutions to perturbed discrete Lyapunov equations is discussed. Several upper bounds of the positive definite solutions are obtained when the perturbation parameters are norm-bounded uncertain. In the derivation of the bounds, one only needs to deal with eigenvalues of matrices and linear matrix inequalities, and thus avoids solving high-order algebraic equations. A numerical example is presented.


  • Algebraic Equation
  • Linear Matrix Inequality
  • Linear Matrix
  • Perturbation Parameter
  • Lyapunov Equation


Authors’ Affiliations

Applied Science College, Harbin University of Science and Technology, Harbin, 150080, China


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© D.-Y. Chen and D.-Y.Wang 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.