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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: Research Article Stabilization of Discrete-Time Control Systems with Multiple State Delays | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 24o707 13 pages doi 10.1155 2009 240707 Research Article Stabilization of Discrete-Time Control Systems with Multiple State Delays Medina Rigoberto Departamento de Ciencias Exactas Universidad de Los Lagos Casilla 933 Osorno Chile Correspondence should be addressed to Medina Rigoberto rmedina@ulagos.cl Received 16 March 2009 Accepted 21 June 2009 Recommended by Leonid Shaikhet We give sufficient conditions for the exponential stabilizability of a class of perturbed time-varying difference equations with multiple delays and slowly varying coefficients. Under appropiate growth conditions on the perturbations combined with the freezing technique we establish explicit conditions for global feedback exponential stabilizability. Copyright 2009 Medina Rigoberto. 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 Let us consider a discrete-time control system described by the following equation in Cn x k 1 A k x k A1 k x k - r B kỴu k x k y k k e -r -r 1 . 0 1.1 1.2 where Cn denotes the n-dimensional space of complex column vectors r 1 is a given integer x Z Cn is the state u Z Cm m n is the input Z is the set of nonnegative integers. Hence forward - II Cn is the Euclidean norm A and B are variable matrices of compatible dimensions A1 is a variable n X n-matrix such that sup A1 k TO k 0 1.3 and p is a given vector-valued function that is p k e Cn. 2 Advances in Difference Equations The stabilizability question consists on finding a feedback control law u k L k x k for keeping the closed-loop system x k 1 A k B k L k x k A1 k x k - r 1.4 asymptotically stable in the Lyapunov sense. The stabilization of control systems is one of the most important properties of the systems and has been studied widely by many .
