Discrete-time Bidirectional Associative Memory Research Articles

State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

For a class of discrete-time bidirectional associative memory neural networks (DTBAMNNs) with multiple time-varying delays, the issue of state estimation is studied. By propose a mathematical induction method, we first investigate novel delay-dependent and -independent global exponential stability (GES) criteria of the error system. The obtained GES criteria are described by linear scalar inequalities. Then, a state observer is derived via the theory of generalized matrix inverses. These exponential stability conditions are very simple, which is convenient to verify based on the standard software tools (for example, YALMIP). Finally, we present two illustrative examples to present the effectiveness of the theoretical results.

Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

Global exponential stability analysis of discrete-time BAM neural networks with delays: A mathematical induction approach

The problem of global exponential stability analysis for discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. By using the mathematical induction method, a novel exponential stability criterion in the form of linear matrix inequalities is firstly established. Then stability criteria depending upon only the system parameters are derived, which can easily checked by using the standard toolbox software (e.g., MATLAB). The proposed approach is directly based on the definition of global exponential stability, and it does not involve the construct of any Lyapunov–Krasovskii functional or auxiliary function. For a class of special cases, it is theoretical proven that the less conservative stability criteria can be obtained by using the proposed approach than ones in literature. Moreover, several numerical examples are also provided to demonstrate the effectiveness of the proposed method.

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

Stability of nonlinear Volterra equations

AbstractUsing a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

Stability of bidirectional associative memory neural networks with Markov switching via ergodic method and the law of large numbers

This paper devotes to stability analysis of continuous time and discrete time bidirectional associative memory (BAM) neural networks whose parameters are randomly varying in a finite state Markov chain sense. Based on the ergodic theory of continuous time Markov chain, the matrix measure approach and Lyapunov theory, almost sure stability and exponential stability in the mean square for continuous time BAM neural networks are derived. We also present some new stability results for discrete time BAM neural networks with the help of the law of large numbers. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in stability of neural networks.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks

This paper concerns the existence and exponential stability of periodic solution for the high-order discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. First, we present the criteria for the existence of periodic solution based on the continuation theorem of coincidence degree theory and the Young’s inequality, and then we give the criteria for the global exponential stability of periodic solution by using a non-Lyapunov method. After that, we give a numerical example that demonstrates the effectiveness of the theoretical results. The criteria presented in this paper are easy to verify. In addition, the proposed analysis method is easy to extend to other high-order neural networks.

Robust state estimation for discrete-time BAM neural networks with time-varying delay

This paper is concerned with the robust delay-dependent state estimation problem for a class of discrete-time Bidirectional Associative Memory (BAM) neural networks with time-varying delays. By using the Lyapunov–Krasovskii functional together with linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived for the existence of state estimator such that the error state system is asymptotically stable. More precisely, an LMI-based state estimator and delay-dependent stability criterion for delayed BAM neural networks are developed. The conditions are established in terms of LMIs which can be solved by the MATLAB LMI toolbox. It should be mentioned that all the sufficient conditions are dependent on the upper and lower bounds of the delays. Also, the desired estimator unknown gain matrix is determined in terms of the solution to these LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness and applicability of the obtained results.

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.

Global Robust Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays

In this paper, the global robust exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium point is obtained for this system. The proposed result is less restrictive, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.

Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales

In this paper, we first investigate the existence of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales by the continuation theorem of coincidence degree theory. Then, by constructing a Lyapunov functional, we discuss the global exponential stability of the periodic solution for such neural networks on time scales. The paper unifies periodic discrete-time and continuous-time BAM neural networks under the same framework.

Exponential periodic attractor of discrete-time BAM neural networks with transmission delays

In this paper, we investigate discrete-time bidirectional associative memory (BAM) neural networks with periodic coefficients and transmission delays. By using matrix measure, spectral theory, and contraction theory, some sufficient conditions are attained for the existence of a unique exponential periodic attractor. Finally, computer simulations illustrate the dynamic behavior of the unique exponential periodic attractor. Moreover, the unique exponential periodic attractor is also given precisely. The numerical simulation is performed to show our results.

Global Exponential Stability of Delayed Cohen-Grossberg BAM Neural Networks with Impulses on Time Scales

Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM) neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.

Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays

This paper is concerned with global robust exponential stability for a class of discrete-time interval bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient criterion is proposed for the global robust exponential stability of discrete-time BAM neural networks which contain uncertain parameters with their values being bounded. The proposed LMI-based results are computationally efficient as they can be easily checked via the LMI toolbox. Finally, two examples are provided to demonstrate the effectiveness of the obtained results.

A unified treatment for stability preservation in computer simulations of impulsive BAM networks

This paper is concerned with the stability preservation in computer simulations of an impulsive bidirectional associative memory (BAM) network. The simulations are provided by difference equations formulated from a semi-discretisation technique and impulsive maps as discrete-time representations of the nonlinear impulses which attempt to destabilise the BAM network at fixed moments of time. Prior to producing the computer simulations, the analogue is analysed for its exponential convergence towards a unique equilibrium state. The analysis exploits the method of Lyapunov sequences to derive several sufficient conditions that govern the network parameters and the impulse magnitude and frequency. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. The treatment of the analysis leads us to a relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals.

Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses

This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.

A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays

The discrete-time bidirectional associative memory neural network with periodic coefficients and infinite delays is studied. And not by employing the continuation theorem of coincidence degree theory as other literatures, but by constructing suitable Liapunov function, using fixed point theorem and some analysis techniques, a sufficient criterion is obtained which ensures the existence and global exponential stability of periodic solution for the type of discrete-time BAM neural network. The obtained result is less restrictive to the BAM neural networks than previously known criteria. Furthermore, it can be applied to the BAM neural network which signal transfer functions are neither bounded nor differentiable. In addition, an example and its numerical simulation are given to illustrate the effectiveness of the obtained result.

Discrete-time BAM neural networks with variable delays

This Letter deals with the global exponential stability of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Using a Lyapunov functional, and linear matrix inequality techniques (LMI), we derive a new delay-dependent exponential stability criterion for BAM neural networks with variable delays. As this criterion has no extra constraints on the variable delay functions, it can be applied to quite general BAM neural networks with a broad range of time delay functions. It is also easy to use in practice. An example is provided to illustrate the theoretical development.

Periodic oscillation of discrete-time bidirectional associative memory neural networks

In this paper, a discrete-time bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we give some sufficient conditions ensuring the existence and globally exponential stability of periodic solutions for the discrete-time bidirectional neural networks. An example with the numerical simulations is provided to show the correctness of our analysis.