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As is known to all that the Lyapunov-Krasovskii functional (LKF) has played a vital role in studying the fixed-time (FXT) stability of the time-delayed Filippov discontinuous systems. When investigating the FXT stability of the time-delayed discontinuous systems, the interesting topic is to provide the more relaxed conditions imposed on the LKF and obtain the more accurate settling-time (ST). This paper aims to investigate the new FXT stability lemma with more relaxed conditions for the time-delayed Filippov discontinuous systems. By using some novel inequality techniques and analytical methods, the new FXT stability lemma is established and more accurate ST is estimated. The traditional discussion about $0 < V < 1$ and $V \geq 1$ is not required. For the purpose of validation, FXT stabilization of discontinuous inertial networks with mixed time delays is considered. By using differential inclusions theory and the new FXT stability lemma, the delay-dependent FXT stabilization criteria are derived. It is the first time to derive the delay-dependent FXT stabilization criteria for the discontinuous inertial networks. Finally, examples are given to show the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the absolute stability analysis for uncertain time-delayed Lur systems with sector and slope restricted nonlinearities. New delay-dependent stability criteria are derived via linear matrix inequality (LMI) formulation that can be easily solved by various convex optimization techniques. Sector bounds and slope bounds are employed to a Lyapunov–Krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained. A numerical example shows effectiveness of the proposed stability condition over some existing ones. [Copyright &y& Elsevier]

In this technical note, the problems of robust stochastic stability, stabilization and H∞-control for uncertain neutral stochastic systems with time-delay are investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Delay-dependent sufficient conditions for the above problems are developed in terms of linear matrix inequalities. Four numerical examples are given which illustrate a relatively low conservatism of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the H∞ and generalized H2 filtering problems for a class of delayed neural networks. The time-varying delay is only required to be continuous and bounded. Delay-dependent criteria are proposed such that the resulting filtering error system is globally exponentially stable with a guaranteed H∞ or generalized H2 performance. It is also shown that the designs of the desired filters are achieved by solving a set of linear matrix inequalities, which can be facilitated efficiently by resorting to standard numerical algorithms. It should be noted that, based on a novel bounding technique, several slack variables are introduced to reduce the conservatism of the derived conditions. Three examples with simulation results are provided to illustrate the effectiveness and performance of the developed approaches. [ABSTRACT FROM AUTHOR]

Abstract: In this note, we address the problem of the existence of a unique equilibrium point and present delay-dependent global asymptotical stability for cellular neural networks with time-delay. The LMI-based criteria are checkable easily. An example illustrates that the proposed conditions provide useful and less conservative results for the problem. [Copyright &y& Elsevier]

This paper studies the problems of existence, uniqueness, global asymptotic stability and global exponential stability of the equilibrium of Cohen-Grossberg neural networks with variable delays. An estimation technique based on delay differential inequality with variable coefficients is developed to establish delay-independent/delay-dependent sufficient conditions for global asymptotic/exponential stability. The stability criteria obtained are based on the M-matrix theory. These criteria can be easily checked in practice and do not require that the delays be constant or differentiable. In particular, our delay-independent asymptotic/exponential stability criteria remove a restriction on the amplification functions imposed by the existing results. Furthermore, our delay-dependent exponential stability criteria give explicitly the allowable upper bound on the diagonal delays such that the global stability property of Cohen-Grossberg neural networks can be retained. Thus, our new results are of great importance in design and application of Cohen-Grossberg neural networks with variable delays. The effectiveness of the new results is further illustrated by two numerical examples in comparison with the existing results. [ABSTRACT FROM AUTHOR]