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 About Robust Stability of Dynamic Systems with Time Delays through Fixed Point Theory | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 480187 20 pages doi 2008 480187 Research Article About Robust Stability of Dynamic Systems with Time Delays through Fixed Point Theory M. De la Sen Faculty of Science and Technology University of the Basque Country Leioa Bizkaia Aptdo. 644 de Bilbao 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 22 September 2008 Revised 10 November 2008 Accepted 19 November 2008 Recommended by Andrzej Szulkin This paper investigates the global asymptotic stability independent of the sizes of the delays of linear time-varying systems with internal point delays which possess a limiting equation via fixed point theory. The error equation between the solutions of the limiting equation and that of the current one is considered as a perturbation equation in the fixed- point and stability analyses. The existence of a unique fixed point which is later proved to be an asymptotically stable equilibrium point is investigated. The stability conditions are basically concerned with the matrix measure of the delay-free matrix of dynamics to be negative and to have a modulus larger than the contribution of the error dynamics with respect to the limiting one. Alternative conditions are obtained concerned with the matrix dynamics for zero delay to be negative and to have a modulus larger than an appropriate contributions of the error dynamics of the current dynamics with respect to the limiting one. Since global stability is guaranteed under some deviation of the current solution related to the limiting one which is considered as nominal the stability is robust against such errors for certain tolerance margins. Copyright 2008 M. De la Sen. 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.
