The paper addresses the stability problem of linear time delay system. In the literature, the most popular approach to tackle this problem relies on the use of LyapunovKrasovskii functionals. Many results have proposed new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches use the same trick, the well-known Jensen’s inequa...

In this paper, new delay-independent asymptotic and exponential stability conditions of linear discrete delay systems based on the LyapunovKrasovskii method have been derived. A numerical example has been developed so as to show applicability of the derived results.

Stability of Time-Delay Systems by Keqin Gu, Vladimir L. Kharitonov, and Jie Chen, Birkhäuser, 2003, 353 pp., ISBN 0-8176-4212-9, $79.95. Reviewed by Vladimir Rasvan and Dan Popescu. The destabilizing effects of time delays are well known to control engineers. In fact, robustness against time delay has been an important and challenging problem from the earliest days of classical control. The la...

The paper studies delay-dependent global robust problem for a class of uncertain stochastic delayed neural networks of neutral-type with discrete and distributed delays. Novel stability criteria are obtained in terms of linear matrix inequality (LMI) by employing the LyapunovKrasovskii functional method and using the free-weighting matrices technique. In addition, two examples are given to show...

This paper introduces an explicit reference governor approach for controlling time delay linear systems subject to state and input constraints. The proposed framework relies on suitable invariant sets that can be built using both Lyapunov-Razumikhin and LyapunovKrasovskii arguments. The proposed method is validated both numerically and experimentally using several alternative formulations.

This paper considers the stability of time-varying delay systems. We develop some new integral inequalities which are proved to encompasses the celebrated Jensen’s inequality. These technical tools allow to construct simple LyapunovKrasovskii functionals very efficient in practice. Notice that our procedure is coupled with the use of the reciprocal convexity result in order to reduce the conser...

In this note, we provided an improved way of constructing a LyapunovKrasovskii functional for a linear time delay system. This technique is based on the reformulation of the original system and a discretization scheme of the delay. A hierarchy of Linear Matrix Inequality based results with increasing number of variables is given and is proved to have convergence properties in terms of conservat...

In this note, we study the problem of asymptotic stability of the delay linear systems. More precisely, we examine the conservativity of a widely-used approach of investigation, based on quadratic Lyapunov-Krasovskii functionals. It is shown that the success of this approach implies strong delay-independent stability of the system under study, but is in general a still stronger condition. Also,...

This paper develops a novel robust stability criterion for a class of uncertain neutral-type neural networks with discrete interval and distributed time-varying delays. By constructing a general form of LyapunovKrasovskii functional, using the linear matrix inequality (LMI) approach and introducing some free-weight matrices, the delay-dependent robust stability criteria are derived in terms of ...

In this paper, an adaptive H∞ control scheme is developed to study the antisynchronization behavior of time-delayed chaotic neural networks with unknown parameters. This adaptive H∞ anti-synchronization controller is designed based on LyapunovKrasovskii theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The proposed synchronization method guarante...