Global Robust Exponential Stability of Interval BAM Neural Network with Mixed Delays under Uncertainty

In this paper, a class of interval bidirectional associative memory (BAM) neural networks with mixed delays under uncertainty are introduced and studied, which include many well-known neural networks as special cases. The mixed delays mean the simultaneous presence of both the discrete delay, and the distributive delay. Furthermore, the parameter of matrix is taken values in a interval and controlled by a unknown, but bounded function. By using a suitable Lyapunov–Krasovskii function with the linear matrix inequality (LMI) technique, we obtain a sufficient condition to ensure the global robust exponential stability for the interval BAM neural networks with mixed delays under uncertainty, which is more generalized and less conservative, restrictive than previous results. In the last section, the validity of our stability result is demonstrated by a numerical example.     

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

Global Asymptotic Stability of Periodic Solutions for Neutral-Type Delayed BAM Neural Networks by Combining an Abstract Theorem of k-Set Contractive Operator with LMI Method

Neural Processing Letters - The paper considers the existence and global asymptotic stability of periodic solutions for a class of neutral-type BAM neural networks with time delays. By combining an...     

On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching

In this paper, the stability analysis problem is investigated for stochastic bi-directional associative memory (BAM) neural networks with Markovian jumping parameters and mixed time delays. Both the global asymptotic stability and global exponential stability are dealt with. The mixed time delays consist of both the discrete delays and the distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and the Itô differential rule to establish sufficient conditions for the delayed BAM networks to be stochastically globally exponentially stable and stochastically globally asymptotically stable, respectively. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs). Therefore, the global stability of the delayed BAM with Markovian jumping parameters can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.     

Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays

In this paper, a class of stochastic impulsive high-order BAM neural networks with time-varying delays is considered. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order BAM neural networks.     

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Global Asymptotic Periodic Synchronization for Delayed Complex-Valued BAM Neural Networks via Vector-Valued Inequality Techniques

In this paper, we are concerned with a class of delayed complex-valued BAM neural networks. In stead of using the priori estimate method of periodic solutions, by means of combining Mawhin’s continuation theorem of coincidence degree theory with novel LMI method and some analysis techniques, a novel LMI-based sufficient condition is obtained for the existence of periodic solutions of the delayed complex-valued BAM neural networks. Then by using novel LMI method, a novel sufficient condition on global asymptotic periodic synchronization of above complex-valued BAM neural networks is established.     

Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]     

Global Robust Exponential Stability of Interval General BAM Neural Network with Delays

In this paper, a class of interval general bidirectional associative memory (BAM) neural networks with delays are introduced and studied, which include many well-known neural networks as special cases. By using fixed point technic, we prove an existence and uniqueness of the equilibrium point for the interval general BAM neural networks with delays. By using a proper Lyapunov functions, we get a sufficient condition to ensure the global robust exponential stability for the interval general BAM neural networks with delays, and we just require that activation function is globally Lipschitz continuous, which is less conservative and less restrictive than the monotonic assumption in previous results. In the last section, we also give an example to demonstrate the validity of our stability result for interval neural networks with delays.     

Novel Sufficient Conditions on Periodic Solutions for Discrete-Time Neutral-Type Neural Networks

Neural Processing Letters - In this paper, we consider the existence and global exponential stability of periodic solutions for a class of delayed discrete-time neutral-type neural networks. Novel...     

Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method

In this paper, we are concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed discrete-time BAM neural networks. Instead of using the method of the priori estimate of periodic solutions in existing papers to study periodic solutions of neural networks, by combining Mawhin’s continuation theorem of coincidence degree theory with linear matrix inequality (LMI) method as well as inequality techniques, some novel LMI-based sufficient conditions to guarantee the existence and global asymptotic stability of periodic solutions for the neural networks are established. Our results which are both dependent on time delay and external inputs of the neural networks are new and complementary to the existing papers.     

New stability criteria for BAM neural networks with time-varying delays

In this paper, the exponential stability is investigated for a class of time-delay BAM neural networks (NNs). Time delays of two layers are taken into account separately rather than as a whole with the idea of delay fractioning. Then we generalize the result to time-varying interval delay condition. Exploiting the known constant part of delay sufficiently to estimate the upper bounds, we can derive an improved stability for BAM NNs with time-varying interval delay. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed linear matrix inequality (LMI) conditions.     

New exponential passivity of BAM neural networks with time-varying delays

In this paper, the exponential passivity for bidirectional associative memory (BAM) neural networks with time-varying delays is considered. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative or zero. By constructing new and improved Lyapunov–Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential passivity criterion for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). A numerical example is given to show that the derived condition is less conservative than some existing results given in the literature.

     

Periodic Solution for Fuzzy Cohen–Grossberg BAM Neural Networks with Both Time-Varying and Distributed Delays and Variable Coefficients

In this paper, we investigate the existence and global exponential stability of periodic solution for a general class of fuzzy Cohen–Grossberg bidirectional associative memory (BAM) neural networks with both time-varying and (finite or infinite) distributed delays and variable coefficients. Some novel sufficient conditions for ascertaining the existence, uniqueness, global attractivity and exponential stability of the periodic solution to the considered system are obtained by applying matrix theory, inequality analysis technique and contraction mapping principle. The results remove the usual assumption that the activation functions are bounded and/or continuously differentiable. It is believed that these results are significant and useful for the design and applications of fuzzy Cohen–Grossberg BAM neural networks. Moreover, an example is employed to illustrate the effectiveness and feasibility of the results obtained here.     

Exponential stability and periodic oscillatory solution in BAMnetworks with delays

Both exponential stability and periodic oscillatory solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays. In addition, two examples are given to illustrate the results.     

Global exponential stability results for delayed neural networks of neutral type

In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear-matrix inequality (LMI) approach, we analyse the global exponential stability of delayed neural networks of neutral type. In addition, the examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays

Neural Processing Letters - This paper considers the global exponential stability (GES) of high-order bidirectional associative memory (BAM) neural networks with proportional delays. Here,...     

一类变时滞神经网络的全局指数稳定性

在不要求激活函数有界的前提下,利用Lyapunov泛函方法和线性矩阵不等式(LMI)分析技巧,研究了一类变时滞神经网络平衡点的存在性和全局指数稳定性.给出判别网络全局指数稳定性的判据,推广了现有文献中的一些结果.这些判据具有LMI的形式,进而易于验证.仿真例子表明了所得结果的有效性.     

Pseudo almost periodic solutions of discrete-time neutral-type neural networks with delays

This paper is concerned with discrete-time neutral-type neural networks with delays. The existence and uniqueness results of pseudo almost periodic solutions are established by applying the contraction mapping principal. By using some mathematical analysis techniques, we further obtain the boundness, exponential attractivity and global exponential stability of pseudo almost periodic solutions for the considered networks. Finally, a typical example and the corresponding numerical simulations have been carried out to support our analytic findings.     

Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses

In this paper, the problem of neutral-type impulsive bidirectional associative memory neural networks (NIBAMNNs) with time delays are first established by a Takagi-Sugeno (T-S) fuzzy model in which the consequent parts are composed of a set of NIBAMNNs with interval delays and Markovian jumping parameters (MJPs). Sufficient conditions to check the robust exponential stability of the derived model are based on the Lyapunov-Krasovskii functionals (LKFs) containing some novel triple integral terms, Lyapunov stability theory and employing the free-weighting matrix method. The delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs), which can be very efficiently solved using Matlab LMI control toolbox. Finally, numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results.