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This paper discusses stability of neural networks (NNs) with time-varying delay. Delay-fractioning Lyapunov-Krasovskii functional (LKF) method and convex analysis are applied to establish a new stability condition. Two possible cases for the delay are taken into account when the delay interval is equivalently divided into two subintervals. The maximal allowable delay that ensures global asymptotical...
This paper investigates robust stability of reset control systems with both uncertainties and transmission delays. Firstly, a generalized Lyapunov-Krasovskii theorem is proven. Secondly, the technique of parameter-dependent full-rank right annihilator of matrices is used to deal with the uncertain reset time instants caused by output matrix uncertainties. Based on this, several necessary and sufficient...
This paper gives new contributions to the area of non-Lyapunov (finite time stability, technical stability, practical stability, final stability) for the particular class of linear discrete time delay systems. The idea of attractive practical stability is introduced for the first time. Moreover, based on the matrix inequalities and Lyapunov-like functions, some new sufficient conditions under which...
In this paper, the problem of exponential stabilization of neutral-type neural networks with various activation functions and interval non-differentiable and distributed time-varying delays is considered. The interval time-varying delay function is not necessary to be differentiable. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, the proposed...
Dynamical behavior of neutral neural networks with distributed delays is studied by employing suitable Lyapunov functional, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical neutral neural networks with time delay and some novel asymptotic stability criteria are also derived. The obtained conditions...
Dynamical behavior of neutral neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical neutral neural networks with time delay and some novel asymptotic stability criteria are also derived. The obtained conditions...
This paper discusses the synchronization problem for a class of Lurie type complex dynamical networks with time-varying delay. Based on a Lyapunov-Krasovskii functional, some new delay-dependent synchronization criteria are derived in the form of linear matrix inequalities by employing a delay decomposition and free matrix method. And a strategy for synchronization is presented based on a linear feedback...
In this paper, exponential stability criteria of linear neutral systems with/ without uncertainties are investigated. By applying a change of variable, the Leibniz-Newton formula, integral inequalities and Lyapunov-Krasovskii functionals without adding free matrices, improved exponential stability-delay dependent criteria of the systems are obtained in the form of linear matrix inequality (LMI). At...
In order to alleviate the conservativeness of the robust stability criterion, the delay-dependent stability problem for uncertain T-S fuzzy time-delay systems with interval time-varying delay is to be investigated in this paper. A new Lyapunov-Krasovskii function and a further improved free-weighing matrix approach are used to analyze the stability. A new less conservative robust stability criterion...
The heavy tailed nature in dynamic spectrum networks challenges the applicability of conventional network stability criterions. To encounter this, a new stability criterion, namely moment stability, is introduced, which requires that the queue length of each secondary user has finite moments for every achievable order. Then, the necessary and sufficient conditions for the existence of a resource allocation...
This paper, the robust stability problem of dynamic interval systems with multiple time-delays is considered. Firstly, a kind of equivalent description of the interval matrix is presented. Then by using Lyapunov stability theory and matrix measure approach, several simple sufficient conditions of robust stability for dynamic continuous and discrete interval systems with multiple time-delays are obtained,...
The ultimate boundedness is one of foundational concepts, which plays an important role in investigating the global asymptotic stability, its control and synchronization for dynamical systems. The ultimate boundedness of stochastic Cohen-Grossberg neural networks with time-varying delays is investigated. By employing Lyapunov method and matrix technique, some novel results and criteria on stochastic...
Power system may not return to its original status and become unstable when subjected to small signal disturbance. Conventional small signal stability (SSS) theory is based on linear control system model without time delay and thus it is not fit for power system stability analysis and stabilization design when relatively larger signal transmission delay exists. In order to overcome the limitations...
This paper is concerned with the problem of robust stability of uncertain neutral systems with distributed delays. By Construct a new Lyapunov-Krasovskii functional, using the idea of discrete delay decomposition, delay decomposition approach is adopted both in discrete delay and distribute delay, combined with new Jensen inequality, improved discrete-, distributed delay-dependent stability conditions...
This paper presents an algebraic criterion for the input-to-state stability (ISS) of recurrent neural networks with Markovian switching. The criterion is easy to be verified with the connection weights. A numerical example is given to demonstrate the effectiveness of the proposed criteria.
A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical...
This paper is concerned with analysis problem for the stability of the a stochastic discrete-time neural networks (DNNs) with discrete time-varying delay. By used some novel analysis techniques, stability theory and Lyapunov -Krasovskii function, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally asymptotically stable in mean square...
The paper investigates the problem of robust stability for a class of continuous-time uncertain switched singular systems with multiple-state delays. By the state transformation and a proper Lyapunov-Krasovskii functional, the robust stability criteria and switching law are given.
The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delays is investigated. An improved delay dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs) to ensure a large upper bound for time-delay. A new class of Lyapunov functional is constructed and the known bounds of the delay interval is split in two subintervals to...
In this paper, based on differential inequality technique, we investigate global exponential stability of recurrent neural networks with distributed delays. Some sufficient conditions are derived which ensure the existence, uniqueness, global exponential stability of equilibrium point of the recurrent neural networks. Finally, an example is given to illustrate advantages of our approach.
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