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Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 1, Pages 71-81
http://dx.doi.org/10.1155/S1048953302000072

Investigation of interval stability of linear systems of neutral type of Lyapunov function method

Kiev University, Complex System Simulation Department, Vladimirskay 64, Kiev-33 01033, Ukraine

Received 1 January 1997; Revised 1 March 1999

Copyright © 2002 Hindawi Publishing Corporation. 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.

Abstract

Systems of differential equations with deviating argument of neutral type [1, 3, 8] are used. The mathematical model takes into account not only the previous moments of time, but also the speed of their change. These equations more adequately describe the dynamics of processes, but their investigation faces significant difficulties. The qualitative behavior of solutions of neutral type systems includes the features both, differential and difference equations [2, 9]. Stability investigations require the smallest size of the delay's speed value [7]. Recently, so-called interval, or robust stability theory has received intensive development. It is based on two theorems of V.L. Kharitonov [4, 5] for scalar: equations. However, difficulties have appeared to obtain similar results for systems in vector-matrix form. It is even more complicated to derive conditions of interval stability for systems of differential-difference equations, though there are results for scalar equation in [6, 10].