Stability Of Interval Neural Networks Research Articles

A systematic method for analyzing robust stability of interval neural networks with time-delays based on stability criteria

This paper presents a systematic method for analyzing the robust stability of a class of interval neural networks with uncertain parameters and time delays. The neural networks are affected by uncertain parameters whose values are time-invariant and unknown, but bounded in given compact sets. Several new sufficient conditions for the global asymptotic/exponential robust stability of the interval delayed neural networks are derived. The results can be casted as linear matrix inequalities (LMIs), which are shown to be generalizations of some existing conditions. Compared with most existing results, the presented conditions are less conservative and easier to check. Two illustrative numerical examples are given to substantiate the effectiveness and applicability of the proposed robust stability analysis method.

Switched exponential state estimation and robust stability for interval neural networks with the average dwell time

This paper is concerned with the problem of the exponential state estimation for switched neural networks with uncertain parameters. Based on the theories of the switched systems and available output measurements, the mathematical model of the switched interval estimation error system under the switching rule with average dwell time is established. Multiple Lyapunov–Krasovskii functions are employed to ensure the stability of the switched estimation error system for all admissible time delays; both the existence conditions and the explicit characterization of the desired estimator are derived in terms of linear matrix inequalities. Moreover, the sufficient conditions for guaranteeing the robust exponential stability of switched interval neural networks with discrete and distributed time delays are easily derived. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Stochastic exponential robust stability of interval neural networks with reaction–diffusion terms and mixed delays

The stochastic exponential robust stability is considered for a class of delayed neural networks with reaction–diffusion terms and Markov jumping parameters in this paper. It is assumed that the uncertain weight matrices belong to the given interval matrices. Some sufficient conditions for the stochastic exponential robust stability of the system are established by applying vector Lyapunov function method and M-matrix theory. The obtained results involving the effect of reaction–diffusion improve the existing conditions. Finally, two examples with numerical simulations are given to illustrate the obtained results.

Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov‐Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay‐dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Further analysis on global robust exponential stability of neural networks with time-varying delays

In this paper, an approach based on H-matrix theory and Halanay inequality is developed to present a sufficient condition for global robust exponential stability of interval neural networks with time-varying delays. Theoretic analysis shows that our result includes a previous result derived in the literature. Finally, some numerical examples are given to show the effectiveness of the obtained results.

Improved global robust exponential stability criteria for interval neural networks with time-varying delays

In this paper, by developing a new approach based on H-matrix theory, some improved sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. Theoretic analysis shows that our results improve and generalize some previously published ones. Finally, some numerical examples are given to show the effectiveness of the obtained results.

Delay‐dependent robust stability analysis for interval neural networks with time‐varying delay

AbstractThis article deals with the problem of robust stability for interval neural networks with time‐varying delay. By constructing an appropriate Lyapunov–Krasovskii functional, using the S‐procedure and taking the relationship among the time‐varying delay, its upper bound and their difference into account, some linear matrix inequality(LMI) ‐based delay‐dependent stability criteria are obtained without ignoring any terms in the derivative of the Lyapunov–Krasovskii functional. Finally, two numerical examples are given to demonstrate the effectiveness and benefits of the proposed method. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Holder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.

Global robust exponential stability for interval neural networks with delay

In this paper, new sufficient conditions for globally robust exponential stability of neural networks with either constant delays or time-varying delays are given. We show the sufficient conditions for the existence, uniqueness and global robust exponential stability of the equilibrium point by employing Lyapunov stability theory and linear matrix inequality (LMI) technique. Numerical examples are given to show the approval of our results.

New results of global robust exponential stability of neural networks with delays

In this paper, the global robust exponential stability of interval neural networks with delays is investigated. Employing homeomorphism techniques and Lyapunov functions, we establish some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed neural networks. It is shown that the obtained results improve and generalize the previously published results.

Global robust stability of interval neural networks with multiple time-varying delays

In this paper, the global robust stability is investigated for interval neural networks with multiple time-varying delays. The neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Without assuming both the boundedness on the activation functions and the differentiability on the time-varying delays, a new sufficient condition is presented to ensure the existence, uniqueness, and global robust stability of equilibria for interval neural networks with multiple time-varying delays based on the Lyapunov–Razumikhin technique as well as matrix inequality analysis. Several previous results are improved and generalized, and an example is given to show the effectiveness of the obtained results.

Global robust exponential stability of delayed neural networks

In this paper, the global robust exponential stability of interval neural networks with time delays is investigated. As far as we are aware only, few papers deals with the interval neural networks and focus on the robust exponential stability. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally robust exponentially stable. The proposed LMI conditions can be checked easily by a recently developed algorithms solving LMIs.

Global exponential robust periodicity and stability of interval neural networks with both variable and unbounded delays

By constructing proper vector Lyapunov functions and nonlinear integro-differential inequalities involving both variable delays and unbounded delays, and using M-matrix theory, several sufficient conditions are obtained. These conditions ensure the global exponential robust periodicity and stability of interval neural networks with both variable and unbounded delays. The assumptions on the boundedness of the activation functions and the differentiability of time-varying delays, needed in most other papers, are no longer necessary in the present study. The obtained results in this paper improve and extend those given in the earlier literature.

Global exponential stability of interval neural networks with variable delays

In this work, the conditions ensuring existence, uniqueness, and global exponential stability of the equilibrium point of interval neural networks with variable delays are studied. Applying the idea of the vector Lyapunov function, and M-matrix theory, the sufficient conditions for global exponential stability of interval neural networks are obtained.

Robust Stability of Interval Neural Networks with Multiple Time Delays

Robust Stability of Interval Neural Networks with Multiple Time Delays

A new criterion for global robust stability of interval neural networks with discrete time delays

This paper further studies global robust stability of a class of interval neural networks with discrete time delays. By introducing an equivalent transformation of interval matrices, a new criterion on global robust stability is established. In comparison with the results reported in the literature, the proposed approach leads to results with less restrictive conditions. Numerical examples are also worked through to illustrate our results.

Global robust exponential stability analysis for interval neural networks with time-varying delays

The problem of the global robust exponential stability of interval neural networks with the time-varying delays is investigated. New stability criteria for such problem are derived by an approach combining the Lyapunov–Krasovskii functional with the linear matrix inequality. The effectiveness of the present results is demonstrated by two numerical examples.

Global exponential stability of continuous-time interval neural networks.

This paper addresses global robust stability of a class of continuous-time interval neural networks that contain time-invariant uncertain parameters with their values being unknown but bounded in given compact sets. We first introduce the concept of diagonally constrained interval neural networks and present a necessary and sufficient condition for global exponential stability of these interval neural networks irregardless of any bounds of non-diagonal uncertain parameters in connection weight matrices. Then we extend the robust stability result to general interval neural networks by giving a sufficient condition. Simulation results illustrate the characteristics of the main results.