On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Stability analysis for neural networks with time-varying delay based on quadratic convex combination

In this paper, a novel method is developed for the stability problem of a class of neural networks with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time-varying delay are derived by the newly proposed augmented simple Lyapunov-Krasovski functional. Different from previous results by using the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to Jensen's inequality. A numerical example is provided to verify the effectiveness and superiority of the presented results.

Sampled-data synchronization of chaotic Lur'e systems with time delays

This paper studies the problem of sampled-data control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems with time delays. It is assumed that the sampling periods are arbitrarily varying but bounded. In order to take full advantage of the available information about the actual sampling pattern, a novel Lyapunov functional is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Based on the Lyapunov functional, an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems. The desired sampled-data controller is designed by a linear matrix inequality approach. The effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of Chua's circuit and neural network.

Stability for neural networks with time-varying delays via some new approaches

This paper considers the problem of delay-dependent stability criteria for neural networks with time-varying delays. First, by constructing a newly augmented Lyapunov-Krasovskii functional, a less conservative stability criterion is established in terms of linear matrix inequalities. Second, by proposing novel activation function conditions which have not been proposed so far, further improved stability criteria are proposed. Finally, three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea.

Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov-Krasovskii functional method

This paper is concerned with the synchronization problems for an array of neural networks with hybrid coupling and interval time-varying delay. First, a novel augmented Lyapunov-Krasovskii functional (LKF) method is proposed to develop delay-dependent synchronization criteria for the networks, which makes use of more relaxed conditions by employing the new type of augmented matrices with Kronecker product operation. The proposed method can handle a multitude of Kronecker product operations in the LKF and alleviates the requirements of the positive definiteness of some conditional matrices which are usually considered in the existing methods for complex networks. This leads to a significant improvement in the performance of the synchronization criteria, i.e., less conservative synchronization results can be obtained. Meanwhile, the case of fast time-varying delay can also be handled by the proposed method. Furthermore, based on the derived criteria, a robust synchronization criterion is obtained for the system with uncertainties both in coefficient and coupling matrix terms. Since an expression based on linear matrix inequality is used, the proposed criteria can be easily checked in practice. Finally, numerical examples are provided to show the effectiveness of the proposed method.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Novel exponential stability criteria of high-order neural networks with time-varying delays

The global exponential stability is analyzed for a class of high-order Hopfield-type neural networks with time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-independent and delay-dependent sufficient conditions are presented for the global exponential stability of the equilibrium point of the considered neural networks. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria.