tailieunhanh - báo cáo hóa học:" Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients"

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 Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 956121 20 pages doi 2010 956121 Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients J. Bastinec 1 J. Diblík 1 2 D. Ya. Khusainov 3 and A. Ryvolova1 1 Department of Mathematics Faculty of Electrical Engineering and Communication Technicka 8 Brno University of Technology 61600 Brno Czech Republic 2 Department of Mathematics and Descriptive Geometry Faculty of Civil Engineering Vevebi 331 95 Brno University of Technology 60200 Brno Czech Republic 3 Department of Complex System Modeling Faculty of Cybernetics Taras Shevchenko National University of Kyiv Vladimirskaya Str. 64 01033 Kyiv Ukraine Correspondence should be addressed to J. Dibllk diblik@ Received 6 July 2010 Accepted 12 October 2010 Academic Editor Julio Rossi Copyright 2010 J. Bastinec et al. 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. This paper investigates the exponential-type stability of linear neutral delay differential systems with constant coefficients using Lyapunov-Krasovskii type functionals more general than those reported in the literature. Delay-dependent conditions sufficient for the stability are formulated in terms of positivity of auxiliary matrices. The approach developed is used to characterize the decay of solutions by inequalities for the norm of an arbitrary solution and its derivative in the case of stability as well as in a general case. Illustrative examples are shown and comparisons with known results are given. 1. Introduction This paper will provide estimates of solutions of linear systems of neutral differential equations with constant coefficients and a constant delay x f Dx f - T Ax f Bx t - T where f 0 is an independent .