Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Improved Delay-Derivative-Dependent Stability Analysis for Generalized Recurrent Neural Networks with Interval Time-Varying Delays

Neural Processing Letters - In this paper, the problem of delay-derivative-dependent stability analysis for generalized neural networks with interval time-varying delays is considered. First, we...     

Delay-Dependent Criteria for Global Exponential Stability of Time-Varying Delayed Fuzzy Inertial Neural Networks

Neural Processing Letters - This paper is mainly concerned with global exponential stability of time-varying delayed fuzzy inertial neural networks. Different from previous approaches of variable...     

An Improved Algebraic Criterion for Global Exponential Stability of Recurrent Neural Networks With Time-Varying Delays

This brief paper presents an M-matrix-based algebraic criterion for the global exponential stability of a class of recurrent neural networks with decreasing time-varying delays. The criterion improves some previous criteria based on M-matrix and is easy to be verified with the connection weights of the recurrent neural networks with decreasing time-varying delays. In addition, the rate of exponential convergence can be estimated via a simple computation based on the criterion herein.     

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

时变时滞离散递归神经网络系统的状态估计器设计

研究时滞离散递归神经系统的状态估计问题.通过网络输出对神经元的状态进行估计.在较弱的激活函数假设下,通过构造一个新的Lyapunov泛函,引入一个自由权矩阵,并结合Jensen不等式得到了确保误差系统全局指数稳定的充分条件.所得条件依赖于时变时滞的上界和下界,并以线性矩阵不等式的形式给出.最后的数值算例表明了所提出方法的有效性.     

New Delay-Dependent Stability Results for Neural Networks With Time-Varying Delay

This paper studies the problem of stability analysis for neural networks (NNs) with a time-varying delay. Unlike the previous works, the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Meanwhile, the computational complexity of the newly obtained stability conditions is reduced because less variables are involved. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.     

Global Robust Exponential Stability of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the equilibrium point of interval neural networks with delays are obtained. The delayed Hopfield network, Bidirectional associative memory network and Cellular neural network are special cases of the network model considered in this Letter. This revised version was published online in June 2006 with corrections to the Cover Date.     

Delay-dependent Stability of Recurrent Neural Networks with Time-varying Delay

This paper investigates the delay-dependent stability problem of recurrent neural networks with time-varying delay. A new and less conservative stability criterion is derived through constructing a new augmented Lyapunov-Krasovskii functional (LKF) and employing the linear matrix inequality method. A new augmented LKF that considers more information of the slope of neuron activation functions is developed for further reducing the conservatism of stability results. To deal with the derivative of the LKF, several commonly used techniques, including the integral inequality, reciprocally convex combination, and free-weighting matrix method, are applied. Moreover, it is found that the obtained stability criterion has a lower computational burden than some recent existing ones. Finally, two numerical examples are considered to demonstrate the effectiveness of the presented stability results.     

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

This paper introduces the design of the hyperconic multilayer perceptron (HC-MLP). Complex non-linear decision regions for classification purposes are generated by quadratic hyper-surfaces spawned by the hyperconic neurons in the hidden layer (for instance, spheres, ellipsoids, paraboloids, hyperboloids and degenerate conics). In order to generate quadratic hyper-surfaces, the hyperconic neurons’ transfer function includes the estimation of a quadratic polynomial. The proper assignment of decision regions to classes is achieved in the output layer by using spheres to determine whether a point is inside or outside the spherical region. The particle swarm optimization algorithm is used for training the HC-MLP. The learning of the HC-MLP selects the best conic surface that separates the data set vectors. For illustration purposes, two experiments are conducted using two distributions of synthetic data in order to show the advantages of HC-MLP when the patterns between classes are contiguous. Furthermore a comparison to the traditional multilayer perceptron is carried out to evaluate the complexity (in terms of the number of estimated patterns) and classification accuracy. HC-MLP is the principal component to implement a diagnosis system to detect faults in an induction motor and to implement an image segmentation system. The performance of HC-MLP is compared to other leading algorithms by using 4 databases commonly used in related literature.     

Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays

Neural Processing Letters - This paper presents some new results on the existence, uniqueness and generalized exponential stability of a positive equilibrium for positive recurrent neural networks...     

Global Exponential Synchronization of Memristive Competitive Neural Networks with Time-Varying Delay via Nonlinear Control

Automatically describing contents of an image using natural language has drawn much attention because it not only integrates computer vision and natural language processing but also has practical applications. Using an end-to-end approach, we propose a bidirectional semantic attention-based guiding of long short-term memory (Bag-LSTM) model for image captioning. The proposed model consciously refines image features from previously generated text. By fine-tuning the parameters of convolution neural networks, Bag-LSTM obtains more text-related image features via feedback propagation than other models. As opposed to existing guidance-LSTM methods which directly add image features into each unit of an LSTM block, our fine-tuned model dynamically leverages more text-conditional image features, acquired by the semantic attention mechanism, as guidance information. Moreover, we exploit bidirectional gLSTM as the caption generator, which is capable of learning long term relations between visual features and semantic information by making use of both historical and future contextual information. In addition, variations of the Bag-LSTM model are proposed in an effort to sufficiently describe high-level visual-language interactions. Experiments on the Flickr8k and MSCOCO benchmark datasets demonstrate the effectiveness of the model, as compared with the baseline algorithms, such as it is 51.2% higher than BRNN on CIDEr metric.     

Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay’s inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.     

Finite-Time Stabilization for Static Neural Networks with Leakage Delay and Time-Varying Delay

Neural Processing Letters - The problem of finite-time stabilization (FTS) for static neural networks (SNNs) with leakage delay and time-varying delay is investigated in this paper. By introducing...     

Global Robust Exponential Stability for Interval Delayed Neural Networks with Possibly Unbounded Activation Functions

In this paper, we mainly study the global robust exponential stability of the neural networks with possibly unbounded activation functions. Based on the topological degree theory and Lyapunov functional method, we provide some new sufficient conditions for the global robust exponential stability. Under these conditions, we prove existence, uniqueness and global robust exponential stability of equilibrium point. In the end, some examples are provided to demonstrate the validity of the theoretical results.     

pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

This paper investigates the problem of the pth moment exponential stability for a class of stochastic recurrent neural networks with Markovian jump parameters. With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, some novel sufficient conditions on the pth moment exponential stability of the considered system are derived. The results obtained in this paper are completely new and complement and improve some of the previously known results (Liao and Mao, Stoch Anal Appl, 14:165–185, 1996; Wan and Sun, Phys Lett A, 343:306–318, 2005; Hu et al., Chao Solitions Fractals, 27:1006–1010, 2006; Sun and Cao, Nonlinear Anal Real, 8:1171–1185, 2007; Huang et al., Inf Sci, 178:2194–2203, 2008; Wang et al., Phys Lett A, 356:346–352, 2006; Peng and Liu, Neural Comput Appl, 20:543–547, 2011). Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.     

Further Improvement on Delay-Dependent Global Robust Exponential Stability for Delayed Cellular Neural Networks with Time-Varying Delays

Neural Processing Letters - This paper is concerned with global robust exponential stability for a class of delayed cellular neural networks with time-varying delays. Some new sufficient conditions...     

Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay

In this paper, we introduce some ideas of switched systems into the field of neural networks and a large class of switched recurrent neural networks (SRNNs) with time-varying structured uncertainties and time-varying delay is investigated. Some delay-dependent robust periodicity criteria guaranteeing the existence, uniqueness, and global asymptotic stability of periodic solution for all admissible parametric uncertainties are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Because free weighting matrices are used to express this relationship and the appropriate ones are selected by means of linear matrix inequalities (LMIs), the criteria are less conservative than existing ones reported in the literature for delayed neural networks with parameter uncertainties. Some examples are given to show that the proposed criteria are effective and are an improvement over previous ones.     

Stability Analysis of Discrete-Time Recurrent Neural Networks With Stochastic Delay

This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with stochastic parameters. Improved conditions for the mean square stability of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay dependence. The merit of the proposed conditions lies in its reduced conservatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the proposed conditions.