Asymptotic Stability Of Neural Networks Research Articles

Asymptotical Stability of Riemann-Liouville Nonlinear Fractional Neutral Neural Networks with Time-Varying Delays

In this paper, the asymptotic stability of solutions is investigated for a class of nonlinear fractional neutral neural networks with time-dependent delays which are unbounded. By constructing the appropriate Lyapunov functional, sufficient conditions for asymptotic stability of neural networks are obtained with the help of LMI. An example is presented by using the LMI Toolbox to demonstrate the effectiveness of the obtained results.

Relaxed Stability Criteria for Neural Networks With Time-Varying Delay Using Extended Secondary Delay Partitioning and Equivalent Reciprocal Convex Combination Techniques.

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.

Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays.

This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov-Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov-Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.

Global Asymptotic Stability for a New Class of Neutral Neural Networks

In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.

Global asymptotic stability of neural networks with uncertain parameters and time-varying delay

This paper is concerned with global asymptotically stability problem for a class of neural networks with uncertain parameters and time-varying delay. Using a new proposed inequality called free-matrix-based integral inequality, the new robust criterion is proposed, which is expressed by linear matrix inequalities, by means of linear matrix inequality technique to deal with the unknown parameters in the neutral systems. An example is simulated to demonstrate the effectiveness and efficiency of the obtained criterion.

Global asymptotic stability of neural networks with uncertain parameters and time-varying delay

This paper is concerned with global asymptotically stability problem for a class of neural networks with uncertain parameters and time-varying delay. Using a new proposed inequality called free-matrix-based integral inequality, the new robust criterion is proposed, which is expressed by linear matrix inequalities, by means of linear matrix inequality technique to deal with the unknown parameters in the neutral systems. An example is simulated to demonstrate the effectiveness and efficiency of the obtained criterion.

An analysis of global robust stability of delayed dynamical neural networks

This paper studies the problem of establishing robust asymptotic stability of neural networks with multiple time delays and in the presence of the parameter uncertainties of the network. A new sufficient condition ensuring robust asymptotic stability is presented by manipulating the properties of some certain classes of real matrices and employing Homomorphic mapping and Lyapunov stability theorems. A numerical example is given to show that the condition obtained can outperform alternative ones in terms of conservatism and computational complexity.

Less conservative stability criteria for neural networks with interval time-varying delay based on delay-partitioning approach

This paper is concerned with the problem of delay-dependent asymptotic stability for neural networks with interval time-varying delay. A delay-partitioning approach is used in this paper, in which the delay interval is partitioned into multiple equidistant subintervals and slightly different Lyapunov–Krasovskii functional is constructed on these intervals. By combining with reciprocally convex approach, several less conservative delay-dependent stability criteria are derived in terms of linear matrix inequality. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method.

Global stochastic stability analysis for stochastic neural networks with infinite delay and Markovian switching

This paper focuses on the stochastic stability for a novel kind of stochastic neural networks with infinite delay and Markovian switching. By using the Lyapunov method, stochastic analysis technique and M-matrix theory, some simple and easily testable sufficient conditions are presented to ensure the trivial solution is stochastically stable, stochastically asymptotically stable, and globally stochastically asymptotically stable, respectively. As a subsequent result, we develop the conditions that guarantee global stochastic asymptotic stability for stochastic neural networks with infinite delay, as well as global asymptotic stability for neural networks with infinite delay. From the perspective of theory, the derived stability criteria include some existing ones as its special cases, and are thus less conservative. Finally, two examples are given to demonstrate the applicability and effectiveness of the theoretical theorems.

New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach

This brief is concerned with the problem of asymptotic stability of neural networks with time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. Novel stability criteria are derived by employing new Lyapunov–Krasovskii functional and the integral inequality. The developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities. New and less conservative solutions to the global stability problem are provided in terms of feasibility testing. Numerical examples are finally given to demonstrate the effectiveness of the proposed method.

Improved Stability Analysis for Neural Networks with Time‐Varying Delay

This paper concerned the problem of delay‐dependent asymptotic stability for neural networks with time‐varying delay. A new class of Lyapunov functional dividing the interval delay is constructed to derive some new delay‐dependent stability criteria. The obtained criteria are less conservative because free‐weighting matrices method, a convex optimization approach, and a mixed dividing delay interval approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

New LMI‐Based Conditions on Neural Networks of Neutral Type with Discrete Interval Delays and General Activation Functions

The stability analysis of global asymptotic stability of neural networks of neutral type with both discrete interval delays and general activation functions is discussed. New delay‐dependent conditions are obtained by using more general Lyapunov‐Krasovskii functionals. Meanwhile, these conditions are expressed in terms of a linear matrix inequality (LMI) and can be verified using the MATLAB LMI toolbox. Numerical examples are used to illustrate the effectiveness of the proposed approach.

Novel delay-dependent stability criteria for neural networks with interval time-varying delay

The problem of delay-dependent asymptotic stability for neural networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov—Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.

Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays

This paper is concerned with the problem of stability of neural networks with time-varying delays. A novel Lyapunov-Krasovskii functional decomposing the delays in all integral terms is proposed. By exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals, some new generalized delay-dependent stability criteria are established, which are different from the existing ones and improve upon previous results. Numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method.

Delay-dependent stability of neural networks of neutral type with time delay in the leakage term

This paper studies the global asymptotic stability of neural networks of neutral type with mixed delays. The mixed delays include constant delay in the leakage term (i.e. ‘leakage delay’), time-varying delays and continuously distributed delays. Based on the topological degree theory, Lyapunov method and linear matrix inequality (LMI) approach, some sufficient conditions are derived ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by the MATLAB LMI toolbox. Even if there is no leakage delay, the obtained results are less restrictive than some recent works. It can be applied to neural networks of neutral type with activation functions without assuming their boundedness, monotonicity or differentiability. Moreover, the differentiability of the time-varying delay in the non-neutral term is removed. Finally, two numerical examples are given to show the effectiveness of the proposed method.

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov–Krasovskii functional

In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities (LMIs) by constructing new Lyapunov–Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

Global asymptotic stability of neural networks with discontinuous activations

Without assuming the boundedness and monotonicity of the neuron activations, we discuss the dynamics of a class of neural networks with discontinuous activation functions. The Leray-Schauder theorem of set-valued maps is successfully employed to derive the existence of an equilibrium point. A Lyapunov-like approach is applied to differential equations with discontinuous right-hand sides modeling the neural network dynamics, which yields conditions for global convergence or convergence in finite time. The obtained results extend previous works on global stability of neural networks with continuous neuron activations or discontinuous neuron activations.

Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks

This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov-Krasovskii functional (LKF) method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz-Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.

Asymptotic stability for neural networks with mixed time-delays: The discrete-time case

This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By constructing a new Lyapnuov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.

New results on global asymptotic stability analysis for neural networks with time-varying delays

This note provides new results on global asymptotic stability for neural networks with time-varying delay. Two types of time-varying delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing an augmented Lyapunov–Krasovskii functional, new delay-dependent stability criteria for delayed neural networks are derived in terms of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.