Exponential Stability In Lagrange Sense Research Articles

A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

This paper mainly studies the global exponential stability in Lagrange sense (GESLS) of quaternion memristive neural networks (QMNNs) with leakage delays, unbounded distributed delays and time-varying discrete time delays. In the process of research, instead of traditional decomposition into real-valued memristive neural networks (RMNNs) or complex-valued memristive neural networks (CMNNs), we consider the QMNN as a whole, and then give a sufficient condition related to time delays to ensure that the considered QMNN is GESLS. An example is provided to illustrate validity of theoretical results obtained in the end. The method proposed in the present text has two merits: (1) According to the definition of GESLS directly, no Lyapunov–Krasovskii functional (LKF) is required, which avoids massive calculations and solutions of high-dimensional matrix inequalities; (2) It is available not only to QMNNs, but also to RMNNs and CMNNs.

Global exponential stability of memristor based uncertain neural networks with time-varying delays via Lagrange sense

ABSTRACT This paper addresses the global exponential stability in Lagrange sense for memristor-based neural networks (MNNs) with time-varying delays. This paper attempts to derive the delay-dependent Lagrange stability conditions in terms of linear matrix inequalities by designing a suitable Lyapunov-Krasovskii functionaland used Wirtinger inequality, Jensen-based inequality for estimating the integral inequalities. The conditions which are derived confirms the globally exponential stability in Lagrange sense for the proposed MNNs and, the detailed estimation for global exponential attractive set is also given. To show the effectiveness and applicability of the proposed criteria, two numerical examples are also provided in this paper.

Discrete analogue of impulsive recurrent neural networks with both discrete and finite distributive asynchronous time-varying delays.

This paper studies the dynamical characteristics of discrete analogue of impulsive recurrent neural networks with both discrete and finite distributed asynchronous time-varying delays. Firstly, the discrete impulsive system of the corresponding continuous-time model is reformed by impulsive maps and semi-discrete method. Secondly, by employing a famous delay impulsive differential inequality, several novel sufficient conditions are derived to ensure the uniqueness of equilibrium point and its global exponential stability in Lagrange sense for the discussed discrete-time impulsive system. Meanwhile, it is illustrated that the discrete-time analogue retains the uniqueness of equilibrium point of the corresponding continuous-time model, and some corollaries follow. Finally, one example is given to demonstrate the validity of our obtained results.

Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

Global exponential stability in Lagrange sense for quaternion-valued neural networks with leakage delay and mixed time-varying delays

ABSTRACTThis paper deals with the global exponential stability in Lagrange sense for quaternion-valued neural networks (QVNNs) with leakage delay, discrete time-varying delays and distributed delays. By structuring an advisable Lyapunov–Krasovskii functional in quaternion field, and adopting free-weighting-matrix method and inequality technique, a sufficient condition in quaternion-valued linear matrix inequality (LMI) to guarantee the global exponential stability in Lagrange sense is acquired, and the domain of attraction is estimated. A numerical example with simulations is supplied to confirm the availability and feasibility of the raised result.

Global exponential stability in Lagrange sense for periodic neural networks with various activation functions and time-varying delays

Global exponential stability in Lagrange sense for periodic neural networks with various activation functions and time-varying delays

Exponential stability in Lagrange sense for inertial neural networks with time-varying delays

This paper addresses the global exponential stability in Lagrange sense for inertial neural networks (INNs) with time-varying discrete delays and distributed delays. By utilizing a proper variable substitution to transform the original system into a first-order differential system, choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality, Jensen-based inequality, Wirtinger-based integral inequality and improved reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the global exponential stability in Lagrange sense for the INNs, are newly obtained in terms of linear matrix inequalities. Meanwhile, the detailed estimation for global exponential attractive set is also given. And two numerical examples are provided to validate the effectiveness of the proposed results.

Global Lagrange Stability for Takagi-Sugeno Fuzzy Cohen-Grossberg BAM Neural Networks with Time-varying Delays

This paper concerns the globally exponential stability in Lagrange sense for Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg BAM neural networks with time-varying delays. Based on the Lyapunov functional method and inequality techniques, two different types of activation functions which include both Lipschitz function and general activation functions are analyzed. Several sufficient conditions in linear matrix inequality form are derived to guarantee the Lagrange exponential stability of Cohen-Grossberg BAM neural networks with time-varying delays which are represented by T-S fuzzy models. Finally, simulation results demonstrate the effectiveness of the theoretical results.

Lagrange Stability for T–S Fuzzy Memristive Neural Networks with Time-Varying Delays on Time Scales

The existed results of Lagrange stability for neural networks (NNs) are scale-free, and hence, conservativeness appears naturally. A class of Takagi–Sugeno (T–S) fuzzy memristive NNs (FMNNs) with time-varying delays is considered on time scales. First, a class of FMNNs is formulated using characteristics of memristors and T–S fuzzy rules. Then some new scale-limited criteria of global exponential stability in Lagrange sense are obtained for FMNNs with bounded feedback functions on the basis of inequalities on time scales and inequality scaling techniques. Also, novel criteria for Lurie-type feedback functions are given, which mainly employ the constructed scale-limited generalized Halanay inequality. Moreover, by matrix-norm strategies, some matrix-norm-based scale-limited criteria are derived for bounded and Lurie-type feedback functions, respectively. It also can be seen that the matrix-norm-based criteria are in accordance with the matrix-measure-based conditions provided the time scale is specified as real set. All scale-limited criteria for Lagrange stability not only include continuous-time criteria and its discrete-time analogues, but also contain more complex cases such as the arbitrary combination of them. In the end, some numerical simulations exhibit the validity of the obtained results.

Discrete Analogue for a Class of Impulsive Cohen–Grossberg Neural Networks with Asynchronous Time-Varying Delays

This paper presents the exponential stability preservation in simulations of an impulsive Cohen–Grossberg neural networks with asynchronous time delays. By semi-discrete technique and impulsive maps as discrete representations of the nonlinear impulsive networks, difference equations formulated is obtained. And developing a new delay impulsive discrete time differential inequality, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence in Lyapunov sense of the discussed discrete time delayed Cohen–Grossberg system. It is show that the discrete time technique can preserve the equilibrium point of the continuous time model. Finally, one numerical example with simulation shows the effectiveness of the obtained results.

Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays

This paper discusses the stability in Lagrange sense for complex-valued neural networks with time-varying discrete delays and distributed delays as well as leakage delay. By constructing an appropriate Lyapunov–Krasovskii functional, and employing free-weighting-matrix approach and inequality techniques in matrix form, a sufficient criterion to guarantee global exponential stability in Lagrange sense is obtained for the investigated neural networks. The given criterion is delay-dependent and is shown as linear matrix inequalities in complex domain, which can be calculated numerically applying valid YALMIP toolbox in MATLAB. A numerical example is provided to manifest the validity of the proposed result.

Mean-square global exponential stability in Lagrange sense for delayed recurrent neural networks with Markovian switching

The paper discusses the mean-square global exponential stability in Lagrange sense for delayed recurrent neural networks (DRNNs) with Markovian switching. Two different types of activation functions are considered, which include both bounded and unbounded activation functions. By using the vector Lyapunov function and stochastic analysis technique, we establish two L-operator differential inequalities. By employing the two L-operator differential inequalities and vector Lyapunov functions methods, we provide easily verifiable criteria for Lagrange stability in mean-square sense of DRNNs with Markovian switching. Finally, two numerical examples are given to illustrate the efficiency of the derived results.

Global lagrange stability of complex‐valued neural networks of neutral type with time‐varying delays

In this article, the problem of global exponential stability in Lagrange sense of neutral type complex‐valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay‐dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016

Global Lagrange stability for neutral type neural networks with mixed time-varying delays

In this paper, the global exponential stability in Lagrange sense for neutral type neural networks with mixed time-varying delays is studied. By constructing proper Lyapunov functions and using inequality techniques, new delay-dependent succinct criteria are derived to ensure the global exponential Lagrange stability for the aforementioned neural networks. Meanwhile, globally exponentially attractive sets are given out. The results obtained here are more general than some of existing results. Finally, two examples are presented and analyzed to validate our results.

Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays

In this paper, the global exponential stability in Lagrange sense related to inertial neural networks with time-varying delay is investigated. Firstly, by constructing a proper variable substitution, the original system is transformed into the first order differential system. Next, some succinct criteria for the ultimate boundedness and global exponential attractive set are derived via the Lyapunov function method, inequality techniques and analytical method. Meanwhile, the detailed estimations for the global exponential attractive set are established. Finally, the effectiveness of theoretical results has been illustrated via two numerical examples.

Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays

This paper focuses on the globally exponential stability in Lagrange sense for Takagi–Sugeno (T–S) fuzzy Cohen–Grossberg neural networks with time-varying delays. By employing Lyapunov method and delay inequality technique, we analyze two different types of activation functions which include both Lipschitz function and general activation functions, several easily verifiable sufficient criteria about linear matrix inequality form are obtained to guarantee the Lagrange exponential stability of Cohen–Grossberg neural networks with time varying delays which are represented by T–S fuzzy models. Meanwhile, the estimations of the globally exponentially attractive sets are given. Here, the existence and uniqueness of the equilibrium points need not be considered. Finally, two numerical examples with simulations are given to illustrate the effectiveness of the theoretical results.

Exponential convergence and Lagrange stability for impulsive Cohen–Grossberg neural networks with time-varying delays

In this paper, the problem on exponential convergence and Lagrange exponential stability for a class of delayed Cohen–Grossberg neural networks with impulses effects is investigated. To this end, a new delay impulsive differential inequality is established, which improves and generalizes previously known criteria. By using the new inequality and coupling with the Lyapunov method, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential convergence of the state variables of the discussed delayed Cohen–Grossberg neural networks with impulses effects. Meanwhile, the framework of the exponential convergence ball in the state space with a pre-specified convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation show the effectiveness of the obtained results.

New LMI-based Criteria for Lagrange Stability of Cohen-Grossberg Neural Networks with General Activation Functions and Mixed Delays

Abstract In this paper, the problem on Lagrange stability of Cohen-Grossberg neural networks (CGNNs) with both mixed delays and general activation functions is considered. By virtue of Lyapunov functional and Halanay delay differential inequality, several new criteria in linear matrix inequalities (LMIs) form for the global exponential stability in Lagrange sense of CGNNs are obtained. Meanwhile, the limitation on the activation functions being bounded, monotonous and differentiable is released, which generalizes and improves those existent results. Moreover, detailed estimations of the globally exponentially attractive sets are given out. It is also verified that outside the globally exponentially attractive set, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the CGNNs. Finally, two numerical examples are given to demonstrate the theoretical results.

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, we study the global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criterions in linear matrix inequality form for the global exponential stability in a Lagrange sense of the neural networks are obtained by virtue of Lyapunov functions and Halanay delay differential inequality. Meanwhile, the estimations of the globally exponentially attractive sets are given out. The results derived here are more general than that of the existing reference. Finally, two examples are given and analyzed to demonstrate our results.

Global exponential stability in Lagrange sense for periodic neural networks with various activation functions

In this paper, global exponential stability in Lagrange sense for periodic neural networks with various activation functions is further studied. By constructing appropriate Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. These theoretical analysis can narrow the search field of optimization computation, associative memories, chaos control and provide convenience for applications.