Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

The paper is concerned with a stability analysis problem for neural networks with Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process, which are governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrix P_i is introduced in this paper. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the lower conservatism and the effectiveness of the proposed LMI conditions.     

Delay decomposition approach to state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters

This paper investigates the state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. On the basis of the new Lyapunov–Krasovskii functional, some inequality techniques, stochastic stability theory and delay‐dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

In this paper, based on the topological degree theory, Lyapunov functional method and inequality analysis technique, the existence and global exponential stability of equilibrium of impulsive fuzzy Cohen–Grossberg bi‐directional associative memory neural networks with delays, are investigated. Moreover, an illustrative example is given to demonstrate the effectiveness of the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Robust asymptotic state estimation of Takagi–Sugeno fuzzy Markovian jumping Hopfield neural networks with mixed interval time‐varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the state estimation of uncertain Markovian jumping Hopfield neural networks with mixed interval time‐varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error are globally asmptotically stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay‐dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally a numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks

This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Stability criteria for stochastic Takagi‐Sugeno fuzzy Cohen‐Grossberg BAM neural networks with mixed time‐varying delays

This article is concerned with the asymptotic stability analysis of Takagi–Sugeno stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed time‐varying delays. Based on the Lyapunov functional and linear matrix inequality (LMI) technique, sufficient conditions are derived to ensure the global convergence of the equilibrium point. The proposed conditions can be checked easily by LMI Control Toolbox in Matlab. It has been shown that the results are less restrictive than previously known criteria. They are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. Numerical examples are given to demonstrate the effectiveness of our results. © 2014 Wiley Periodicals, Inc. Complexity 21: 143–154, 2016     

New delay‐dependent global robust passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays

The problem of passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays is investigated in this article. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay‐decomposing idea and using improved free‐weighting matrix method, some improved delay‐dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 167–179, 2016     

Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays

In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov-Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.     

Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov–Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.     

Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities

The stochastic finite-time boundedness problem is considered for a class of uncertain Markovian jumping neural networks (MJNNs) that possess partially known transition jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By selecting the appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions of stochastic finite time boundedness of MJNNs are presented and proved. The boundedness criteria are formulated in the form of linear matrix inequalities and the designed algorithms are described as optimization ones. Simulation results illustrate the effectiveness of the developed approaches.     

Stability analysis in Lagrange sense for a non-autonomous Cohen–Grossberg neural network with mixed delays

The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.     

Robust stability for stochastic Hopfield neural networks with time delays

In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

Stability and Hopf bifurcation of a delayed Cohen–Grossberg neural network with diffusion

In this paper, a delayed Cohen–Grossberg neural network with diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation at the trivial steady state are established, respectively. By using the normal form theory and the center manifold reduction of partial function differential equations, formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters

This paper investigates the delay-dependent global asymptotic stability problem of stochastic genetic regulatory networks (SGRNs) with Markovian jumping parameters. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are globally asymptotically stable in the mean square. Distinct difference from other analytical approaches lies in “linearization” of the genetic regulatory networks (GRNs) model, by which the considered GRN model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation is used to transform the linear system. Novel criteria for global asymptotic stability of the SGRNs with constant delays are obtained. Some numerical examples are given to illustrate the effectiveness of our theoretical results.