Class Of Neutral-type Neural Networks Research Articles

Global attractive periodic solutions of neutral-type neural networks with delays in the leakage terms

<abstract><p>In this paper, we introduce a class of neutral-type neural networks with delay in the leakage terms. Using coincidence degree theory, Lyapunov functional method and the properties of neutral operator, we establish some new sufficient criteria for the existence and global attractiveness of periodic solutions. Finally, an example demonstrates our findings.</p></abstract>

Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays

The key contribution of this paper is to study the stability analysis of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a proper Lyapunov functional, we propose a novel sufficient time-independent stability criterion for this model of neutral-type neural networks. The proposed stability criterion in this paper can be absolutely expressed in terms of the parameters of the neural network model considered as this newly proposed criterion only relies on the relationships established among the network parameters. A numerical example is also given to indicate the advantages of the obtained stability criterion over the previously published stability results for the same class of Cohen-Grossberg neural networks. Since obtaining stability conditions for neutral-type Cohen-Grossberg neural networks with multiple delays is a difficult task to achieve, there are only few papers in the literature dealing with this problem. Therefore, the results given in the current paper makes an important contribution to the stability problem for this class of neutral-type neural networks.

Stability analysis of Cohen–Grossberg neural networks of neutral-type: Multiple delays case

The essential purpose of this work is to conduct an investigation into stability problem for the class of neutral-type Cohen–Grossberg neural networks including multiple time delays in states and multiple neutral delays in time derivative of states. By proposing an appropriate Lyapunov functional, a new sufficient criterion is derived for global asymptotic stability of neutral-type neural networks. The obtained stability criterion is independent of time delay and neutral delay parameters, and it is completely stated in terms of the elements of interconnection matrices and other network parameters. Thus, this newly presented stability condition can be validated by simply examining some algebraic equations establishing some relationships among the system parameters and matrices of the neutral-type neural system. A constructive example is presented to indicate applicability of the obtained sufficient stability condition. Since stability analysis of the class of neutral-type neural networks considered in this work has not been given much attention due to the difficulty of developing efficient mathematical techniques and methods enabling to conduct a stability analysis of such neutral-type neural systems, the criterion proposed in this paper can be considered as a leading stability result for neutral-type Cohen–Grossberg neural systems including multiple time and multiple neutral delays.

Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump

In this paper, the stochastic stability problem for a class of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump is discussed. The uncertainty of semi-Markov jump refers to that the partial information on transition rates are incompletely known. Firstly, an extended reciprocally convex combination inequality with less conservative is provided. Secondly, by constructing an eligible stochastic Lyapunov–Krasovskii functional with considering more information about various time delays, uncertain semi-Markov jumping parameters, some stability criterions are derived via utilizing the improved inequality together with some integral inequalities. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays

This paper is concerned with a class of neutral-type neural networks with discontinuous activations and time-varying delays. Under the concept of Filippov solution, by applying the differential inclusions and the topological degree theory in set-valued analysis, we employ a novel argument to establish new results on the existence of the periodic solutions for the considered neural networks. After that, we derive some criteria on the uniqueness, global exponential stability of the considered neural networks and convergence of the corresponding autonomous case of the considered neural networks, in terms of nonsmooth analysis theory with Lyapunov-like approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, the results obtained can also be valid. Our results extend previous works on the neutral-type neural networks to the discontinuous cases, some related results in the literature can be enriched and extended. Finally, two typical examples and the corresponding numerical simulations are provided to show the effectiveness and flexibility of the results derived in this paper.

Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin's continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained.

Design of exponential state estimators for neutral-type neural networks with mixed time delays

In this paper, the state estimation problem is dealt with for a class of neutral-type neural networks with mixed time delays. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

Almost periodic solution for a neutral-type neural networks with distributed leakage delays on time scales

By using exponential dichotomy theory, contraction mapping principle and discrete-continuous analysis method, we obtain some new sufficient conditions ensuring the existence and global exponential stability of the almost periodic solutions for a class of neutral-type neural networks with distributed leakage delays on time scales. An example is provided to demonstrate the usefulness of the main results obtained.

An analysis of stability of neutral-type neural systems with constant time delays

This paper investigates the stability problem of a class of neutral-type neural networks with constant time delays. By constructing a proper Lyapunov functional, a novel sufficient condition for the global stability of the equilibrium point for the class of neutral-type neural systems is presented. The obtained stability condition is expressed in terms of the system parameters of the network, and therefore, it can be easily verified. We also give a comparative numerical example to show the applicability of the result and demonstrate its advantages over the previously published corresponding stability results.

Exponential Stabilization of Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays by Intermittent Control: A CCL Approach

For a class of neutral-type neural networks with discrete and distributed delays, the problem of exponential stabilization is studied in this paper by using periodically intermittent control. By introducing an appropriate Lyapunov–Krasovskii functional and using matrix inequality techniques to deal with its derivative, exponential stabilization criteria are presented in the form of nonlinear matrix inequalities. In order to solve the nonlinear problem, a cone complementarity liberalization (CCL) algorithm is proposed. In addition, numerical examples are provided to illustrate the applicability of the proposed approach.

Robust passive filtering for neutral-type neural networks with time-varying discrete and unbounded distributed delays

The passive filtering problem is studied for a class of neutral-type neural networks with time-varying discrete and unbounded distributed delays. Based on the passive theory, a sufficient condition for the existence of the robust passive filter is given. By introducing an appropriate Lyapunov–Krasovskii functional and using Jensen's inequality technique to deal with its derivative, the criterion which ensures error dynamic system to be strictly passive with dissipation γ>0 is presented in the form of nonlinear matrix inequality. In order to solve the nonlinear problem, a cone complementarity linearization (CCL) algorithm is proposed. Furthermore, when the norm-bounded parameter uncertainties appear in the class of neural networks, the corresponding robust passive filtering problem is also investigated. Three examples are given to demonstrate the effectiveness of the proposed method.

An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays

The problem of existence, uniqueness, and global asymptotic stability is considered for the class of neutral-type neural network model with discrete time delays. By employing a suitable Lyapunov functional and using the homeomorphism mapping theorem, we derive some new delay-independent sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point for this class of neutral-type systems. The obtained conditions basically establish some norm and matrix inequalities involving the network parameters of the neural system. The main advantage of the proposed results is that they can be expressed in terms of network parameters only. Some comparative examples are also given to compare our results with the previous corresponding results and demonstrate the effectiveness of the results presented.

Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays

This paper is concerned with the stability problem for a class of Markovian jumping neutral-type neural networks with mode-dependent mixed time-delays. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. In addition, the distributed time-delays are characterized by the upper and lower bounds, both of which are mode-dependent. By constructing new Lyapunov–Krasovskii functionals, a unified framework is established to derive sufficient conditions for the concerned systems to be globally exponentially stable in mean square. A simulation example is provided to demonstrate the usefulness of the main results obtained.

State Feedback Stabilization for Neutral-Type Neural Networks with Time-Varying Discrete and Unbounded Distributed Delays

The problem of stabilization for a class of neutral-type neural networks with discrete and unbounded distributed delays is investigated. By introducing an appropriate Lyapunov-Krasovskii functional and using Jensen inequality technique to deal with its derivative, delay-range-dependent and rate-dependent stabilization criteria are presented in the form of LMIs with nonlinear constraints. In order to solve the nonlinear problem, a cone complementarity linearization (CCL) algorithm is offered. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach.

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.

Novel Delay-Dependent Robust Stability Analysis for Switched Neutral-Type Neural Networks With Time-Varying Delays via SC Technique

This paper studies a class of new neural networks referred to as switched neutral-type neural networks (SNTNNs) with time-varying delays, which combines switched systems with a class of neutral-type neural networks. The less conservative robust stability criteria for SNTNNs with time-varying delays are proposed by using a new Lyapunov-Krasovskii functional and a novel series compensation (SC) technique. Based on the new functional, SNTNNs with fast-varying neutral-type delay (the derivative of delay is more than one) is first considered. The benefit brought by employing the SC technique is that some useful negative definite elements can be included in stability criteria, which are generally ignored in the estimation of the upper bound of derivative of Lyapunov-Krasovskii functional in literature. Furthermore, the criteria proposed in this paper are also effective and less conservative in switched recurrent neural networks which can be considered as special cases of SNTNNs. The simulation results based on several numerical examples demonstrate the effectiveness of the proposed criteria.

New results for global stability of a class of neutral-type neural systems with time delays

This paper studies the global convergence properties of a class of neutral-type neural networks with discrete time delays. This class of neutral systems includes Cohen–Grossberg neural networks, Hopfield neural networks and cellular neural networks. Based on the Lyapunov stability theorems, some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral-type systems are derived. It is shown that the results presented in this paper for neutral-type delayed neural networks are the generalization of a recently reported stability result. A numerical example is also given to demonstrate the applicability of our proposed stability criteria.

Globally Asymptotic Stability of a Class of Neutral-Type Neural Networks With Delays

Several stability conditions for a class of systems with retarded-type delays are presented in the literature. However, no results have yet been presented for neural networks with neutral-type delays. Accordingly, this correspondence investigates the globally asymptotic stability of a class of neutral-type neural networks with delays. This class of systems includes Hopfield neural networks, cellular neural networks, and Cohen-Grossberg neural networks. Based on the Lyapunov stability method, two delay-independent sufficient stability conditions are derived. These stability conditions are easily checked and can be derived from the connection matrix and the network parameters without the requirement for any assumptions regarding the symmetry of the interconnections. Two illustrative examples are presented to demonstrate the validity of the proposed stability criteria.