Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 58931, 8 pages

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

Dong-Yan Chen and De-Yu Wang

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

Received 20 February 2006; Revised 4 June 2006; Accepted 12 June 2006

Copyright © 2006 Dong-Yan Chen and De-Yu Wang. 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.


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.