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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: ON THE ESTIMATION OF UPPER BOUND FOR SOLUTIONS OF PERTURBED DISCRETE LYAPUNOV EQUATIONS | ON THE ESTIMATION OF UPPER BOUND FOR SOLUTIONS OF PERTURBED DISCRETE LYAPUNOV EQUATIONS DONG-YAN CHEN AND DE-YU WANG Received 20 February 2006 Revised 4 June 2006 Accepted 12 June 2006 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. Copyright 2006 D.-Y. Chen and D.-Y. 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. 1. Introduction Consider the following perturbed discrete Lyapunov equation for the variable matrix P e RnXn P A AA TP A AA Q 1.1 where the matrix A e RnXn is given AA e RnXn is an uncertain matrix which represents the structure disturbance of A and Q e RnXn is a symmetric positive definite or semidef-inite matrix. Assume that AA satisfies the norm-bounded uncertainty AA DFE 1.2 where D and E are given constant matrices of appropriate dimensions and F is an unknown real time-varying matrix with Lebesgue measurable entries satisfying FTF I with I being an identity matrix of appropriate dimension. Furthermore we assume that A is asymptotically stable. The discrete Lyapunov equation 1.1 plays an indispensable role in many areas of science and technology such as system design signal processing and optimal control and so forth. Hence the investigation on its solutions is very important. Recently there have Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 58931 Pages 1-8 DOI 10.1155 JIA 2006 58931 2 Upper bound to perturbed DLE been a lot of results obtained on this
