Narrow Results

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.

In this paper, the problem of global robust exponential stabilization for a class of neural networks with reaction-diffusion terms and time-varying delays which covers the Hopfield neural networks and cellular neural networks is investigated. A feedback control gain matrix is derived to achieve the global robust exponential stabilization of the neural networks by using the Lyapunov stability theory, and the stabilization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Finally, a numerical simulation illustrates the effectiveness of the results.

This paper investigates the problem of stability analysis for recurrent neural networks with time-varying delays and polytopic uncertainties. Parameter-dependent Lypaunov functionals are employed to obtain sufficient conditions that guarantee the robust global exponential stability of the equilibrium point of the considered neural network. The derived stability criteria are expressed in terms of a set of relaxed linear matrix inequalities, which can be easily tested by using commercially available software. Two numerical examples are provided to demonstrate the effectiveness of the proposed results.

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

A general model for an array of discrete-time neural networks with hybrid coupling is proposed, which is composed of nonlinear coupling and time-varying delays. The coupling terms are described in terms of Lipchitz-type conditions that reflect more realistic dynamical behaviors of coupled systems in practice. The properties of Kronecker product are employed in order to pursue mathematical simplicity of dynamics analysis. On the basis of Lyapunov stability theory, an effective matrix functional is utilized to establish sufficient conditions under which the considered neural networks are globally synchronized. These conditions, which are dependent on the lower bound and the upper bound of the time-varying time delays, are expressed in terms of several linear matrix inequalities (LMIs), and therefore can be easily verified by utilizing the numerically efficient Matlab LMI toolbox. One illustrative example is given to justify the validity and feasibility of the proposed synchronization scheme.

In this paper, the problem of stability analysis of neural networks with discrete time-varying delays is considered. By constructing a new Lyapunov functional and some novel analysis techniques, new delay-dependent criteria for checking the asymptotic stability of the neural networks are established. The criteria are presented in terms of linear matrix inequalities, which can be easily solved and checked by various convex optimization algorithms. Three numerical examples are included to show the superiority of our results.

In this paper, finite-time synchronization for a class of complex-valued coupled chaotic systems with bounded non-identical perturbations and discontinuous activations is investigated. State feedback controller and Lyapunov function are designed to deal with time delay of the coupled systems. By separating the state variables into real and imaginary parts and using chain rule, sufficient conditions are obtained to realize finite-time synchronization. Moreover, the setting time can be estimated for chaotic systems. Those results can be applied to the continuous and real-valued chaotic systems. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

This paper considers the problem of stability analysis for neural networks with time-varying delays. The time-varying delays under consideration are assumed to be bounded but not necessarily differentiable. In terms of a linear matrix inequality, a delay-dependent asymptotic stability condition is developed, which ensures the existence of a unique equilibrium point and its global asymptotic stability. The proposed stability condition is easy to check and less conservative. An example is provided to show the effectiveness of the proposed condition.

In this paper, a class of impulsive fuzzy cellular neural networks (FCNNs) with mixed delays and diffusion is formulated and investigated. By establishing an intergro-differential inequality, applying M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of an equilibrium point for impulsive FCNNs with mixed delays and diffusion. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulses. These results generalize and improve the earlier publications. Some examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of FCNNs.

In this paper, the synchronization problem of Chen systems with time-varying delays is discussed based on the stability theory of time-delay systems. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. And finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

This paper deals with the passivity analysis problem for Takagu-Sugeno (T-S) fuzzy neural networks with mixed interval time-varying delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Delay-dependent sufficient conditions for the passivity problem are obtained by using Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique. The important feature of the results lies in that it does not make use of upper bounds to introduce some degree of conservativeness. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design procedures.

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

Network-based load frequency control (LFC) requires data transmission from the plant site to the control center and control center to the plant site. Communication delays resulting from an open communication network impart time-varying nature to network delay. This time-varying delay may debase the dynamic performance or instability of the LFC systems. Stability of the LFC system is investigated by Lyapunov–Krasovskii functional (LKF) analysis and linear matrix inequalities (LMIs) techniques. In this paper, a less conservative delay-dependent stability criterion is derived for the time-delay system by proper constructing of LKF and imposing tighter bounding of integral terms on time-derivative of LKF. Delay margin is obtained by solving proposed stability criterion for a time-delay LFC system equipped with a proportional-integral controller. The adequacy of the proposed result is confirmed using simulation studies.

This paper investigates the optimal guaranteed cost control of synchronization for uncertain stochastic complex networks with time-varying delays. The aim is to design state-feedback controllers such that the complex networks are globally asymptotical mean-square synchronization, and meanwhile the optimal upper bound of cost function is guaranteed. Based on Lyapunov–Krasovskii stability theory and Itô differential rule, sufficient condition for the existence of the optimal guaranteed cost control laws is given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.

The passivity conditions for stochastic neural networks with time-varying delays and random abrupt changes are considered in this paper. Sufficient conditions on passivity of stochastic neural networks with time-varying delays and random abrupt changes are developed in the linear matrix inequality (LMI) setting. The results obtained in this paper improve and extend some of the previous results.

This paper is devoted to global exponential stability of reaction-diffusion time-varying delayed cellular neural networks with Dirichlet boundary conditions. Without assuming the monotonicity and differentiability of activation functions, nor symmetry of synaptic interconnection weights, the authors present some delay independent and easily verifiable sufficient conditions to ensure the global exponential stability of the equilibrium solution by using the method of variational parameter and inequality technique. These conditions obtained have important leading significance in the designs and applications of global exponential stability for reaction-diffusion neural circuit systems with delays. Lastly, one example is given to illustrate the theoretical analysis.

In this paper, a class of nonautonomous fuzzy cellular neural networks (FCNNs) with reaction-diffusion terms and time-varying delays are investigated. By applying the inequality analysis technique, introducing ingeniously many real parameters and constructing new auxiliary functions, a series of new and useful criteria on the boundedness and globally exponential stability of solutions are established. The results obtained in this paper extend and improve the corresponding results given in previous works. Finally, two examples are given to verify the effectiveness of the obtained results.

A synchronization control scheme is proposed for uncertain coronary artery system (CAS) with input saturation. In order to deal with the input saturation, linear matrix inequalities (LMIS), adequate conditions are obtained based on the local sector condition. Furthermore, by constructing Lyapunov–Krasovskii functional (LKF), we design a state feedback controller to achieve synchronization for chaos system with input saturation. Moreover, the improved Jensen inequality, convex analysis, delay-partitioning approach and Moon et al.’s inequality are utilized to get the less conservative. Finally, the simulation result is given to explain the effectiveness of the proposed synchronization control scheme.