Global Robust Exponential Stability Research Articles

Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Global robust exponential stability for Hopfield neural networks with non-Lipschitz activation functions

We consider the problem of global robust exponential stability for Hopfield neural networks with norm-bounded parameter uncertainties and inverse Holder neuron activation functions. By using the Brouwer degree properties and some analysis techniques, we investigate the existence and uniqueness of an equilibrium point. Based on the Lyapunov stability theory, we derive a global robust exponential-stability criterion in terms of a linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the efficiency and validity of the proposed robust stability results.

Robustness analysis for connection weight matrices of global exponential stability of stochastic recurrent neural networks

This paper analyzes the robustness of global exponential stability of stochastic recurrent neural networks (SRNNs) subject to parameter uncertainty in connection weight matrices. Given a globally exponentially stable stochastic recurrent neural network, the problem to be addressed here is how much parameter uncertainty in the connection weight matrices that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural network to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result.

On the Robust Practical Global Stability of Nonlinear Time-varying Systems

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in 19. The second part provides sufficient conditions for the robust practical globally uniformly asymptotically stability (RpGUAS).

Robustness analysis for connection weight matrix of global exponential stability recurrent neural networks

This paper analyzes the robustness of global exponential stability of recurrent neural networks subject to parameter uncertainty in connection weight matrix. Given a globally exponentially stable recurrent neural network, the problem to be addressed herein is how much parameter uncertainty in the connection weight matrix that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural networks to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result.

Robustness analysis of global exponential stability of neural networks with Markovian switching in the presence of time-varying delays or noises

In this paper, we analyze the robustness of global exponential stability of neural networks with Markovian switching (NNwMS) subject to random disturbances or time-varying delays. Given a globally exponentially stable neural network with Markovian switching, the problems to be addressed herein are how much noises or time delays that the neural networks can remain to be globally exponentially stable. We characterize the upper bounds of the time delays or noise intensity for the NNwMS to sustain global exponential stability. Two numerical examples are provided to illustrate the theoretical results.

Stability analysis of impulsive parabolic complex networks with multiple time-varying delays

In the present paper, a new impulsive parabolic complex network (IPCN) with time-varying delays is proposed. Then, by constructing appropriate Lyapunov functionals and utilizing inequality techniques, some sufficient conditions are given to ensure that the proposed network model is globally exponentially stable. Furthermore, when the parameter uncertainties appear in the IPCN, several robust global exponential stability conditions are also presented. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of our criteria.

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.

Global Robust Exponential Stability of Cohen-Grossberg Neural Network with Time Varying Delays

In this paper, the global robust exponential stability is discussed for Cohen-Grossgerg neural network with parameter uncertainties and time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The proposed result is less restrictive, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

Robust stability analysis of interval fuzzy Cohen–Grossberg neural networks with piecewise constant argument of generalized type

In this paper, existence and uniqueness of the solution of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument are discussed. Based on the comparison principle, it presents new theoretical results on the global robust exponential stability of interval fuzzy Cohen-Grossberg networks with piecewise constant argument. As a special case, the corresponding results of interval fuzzy recurrent neural networks with piecewise constant argument are derived. Three examples are given for illustrating validity of the obtained results.

Robust stability and robust passivity of parabolic complex networks with parametric uncertainties and time-varying delays

In this paper, the robust global exponential stability and robust passivity are investigated for a class of parabolic complex networks with multiple time-varying delays. By constructing appropriate Lyapunov functionals and utilizing inequality techniques, several criteria for robust global exponential stability and robust passivity are established. Finally, a numerical example is also given to illustrate the effectiveness of the obtained results.

Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

A class of interval neural networks with time‐varying delays and distributed delays is investigated. By employing H‐matrix and M‐matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

LMI‐Based Approach for Exponential Robust Stability of High‐Order Hopfield Neural Networks with Time‐Varying Delays

This paper studies the problems of global exponential robust stability of high‐order hopfield neural networks with time‐varying delays. By employing a new Lyapunov‐Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high‐order neural networks are established, which are easily verifiable and have a wider adaptive.

Passivity and Stability Analysis of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions

This paper is concerned with the passivity and stability problems of reaction-diffusion neural networks (RDNNs) in which the input and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, some sufficient conditions ensuring the passivity and global exponential stability are derived. Furthermore, when the parameter uncertainties appear in RDNNs, several criteria for robust passivity and robust global exponential stability are also presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

Stability analysis of impulsive parabolic complex networks

In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.

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.

Global exponential robust stability of static interval neural networks with S-type distributed delays

The authors in [7] obtained the global asymptotical stability for static interval neural networks with S-type distributed delays by using the Razumikhin theorem. The aim of our paper is to investigate the global exponential robust stability by using the Lyapunov functional methods, and we will improve the proof methods more concise. A theorem and a corollary were obtained in which the boundedness, monotonicity and differentiability conditions on the activation functions are not required. So we generalize the results of related literature [7]. As an application, an example to demonstrate our results is given.

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.

Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays

In this paper, the problem of robust exponential stability analysis of uncertain discrete-time recurrent neural networks with Markovian jumping and time-varying delays is studied. 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 recurrent neural networks which contain uncertain parameters and Markovian jumping parameters. The obtained stability criterion is characterized in terms of linear matrix inequalities (LMIs) and can be easily checked by utilizing the efficient LMI toolbox. Two numerical examples are presented to show the effectiveness and conservativeness of the proposed method.