Boundary Value Problems
Volume 2010 (2010), Article ID 956121, 20 pages
Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients
1Department of Mathematics, Faculty of Electrical Engineering and Communication, Technická 8, Brno University of Technology, 61600 Brno, Czech Republic
2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Veveří 331/95, Brno University of Technology, 60200 Brno, Czech Republic
3Department of Complex System Modeling, Faculty of Cybernetics, Taras, Shevchenko National University of Kyiv, Vladimirskaya Str., 64, 01033 Kyiv, Ukraine
Received 6 July 2010; Accepted 12 October 2010
Academic Editor: Julio Rossi
Copyright © 2010 J. Baštinec 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.