Further stability analysis on Cohen–Grossberg neural networks with time-varying and distributed delays

The article is concerned with asymptotical stability for Cohen–Grossberg neural networks with both interval time-varying (0?≤?τ₀?≤?τ(t)?≤?τ _m ) and distributed delays, in which two types of distributed delays are treated: one is bounded while the other is unbounded. Through partitioning the delay intervals [0,?τ₀] and [τ₀,?τ _m ], and choosing two augmented Lyapunov–Krasovskii functionals, some sufficient conditions are obtained to guarantee the global stability by employing the simplified free-weighting matrix method and convex combination. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked by resorting to LMI in Matlab toolbox. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of the theoretical results.     

Finite-time stability analysis for fractional-order Cohen–Grossberg BAM neural networks with time delays

In this paper, the problem of finite-time stability for a class of fractional-order Cohen–Grossberg BAM neural networks with time delays is investigated. Using some inequality techniques, differential mean value theorem and contraction mapping principle, sufficient conditions are presented to ensure the finite-time stability of such fractional-order neural models. Finally, a numerical example and simulations are provided to demonstrate the effectiveness of the derived theoretical results.

     

Input-to-state stability of stochastic nonlinear fuzzy Cohen–Grossberg neural networks with the event-triggered control

ABSTRACT

In this paper, we investigate a class of stochastic nonlinear fuzzy Cohen–Grossberg neural networks with feedback control and an unknown exogenous disturbance. By using the Lyapunov function, Itô's formula, Dynkin's formula, Comparison principle and stochastic analysis theory, we show that the considered system is input-to-state stable with the help of the designed event-triggered mechanism. Moreover, we also guarantee that the internal execution time intervals of control task will not be arbitrarily small. Finally, some remarks and discussions have been provided to show that our results are meaningful.     

Almost sure stability of stochastic neutral Cohen–Grossberg neural networks with Lévy noise and time-varying delays

The almost sure stability for the stochastic neutral Cohen–Grossberg neural networks (SNCGNNs) with Lévy noise, time-varying delays, and Markovian switching would be deliberated in this article. By means of the nonnegative semimartingale convergence theorem (NSCT), the neutral Itô formula, M-matrix method, and selecting appropriate Lyapunov function, several almost sure stability criterions for the SNCGNNs could be derived. Moreover, according to the M-matrix theory, the upper bounds of the coefficients at any mode are given. Finally, two examples and numerical simulations verify the correctness of theoretical analysis for the stability criterions proposed in the article.     

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.     

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.     

Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, we study the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. By establishing an L-operator differential inequality with mixed delays and using the properties of M-cone and stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. These results generalize a few previous known results and remove some restrictions on the neural networks. Two examples are also discussed to illustrate the efficiency of the obtained results.     

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

     

Robust H ∞ filter design of uncertain T-S fuzzy neutral systems with time-varying delays

This article addresses the problem of robust H _∞ filter design of a class of Takagi–Sugeno fuzzy neutral systems with time-varying delays and norm-bounded parameter uncertainties. A fuzzy filter is constructed, which ensures both the robust stability and a prescribed H _∞ performance of the filtering error system. A linear matrix inequality approach is developed, and a delay-dependent sufficient condition is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed approach.     

Design of H ∞ control of neural networks with time-varying delays

This paper deals with the H _∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H _∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

     

Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction–diffusion terms

The problem of mean square exponential stability for a class of impulsive stochastic fuzzy cellular neural networks with distributed delays and reaction–diffusion terms is investigated in this paper. By using the properties of M-cone, eigenspace of the spectral radius of nonnegative matrices, Lyapunov functional, Itô’s formula and inequality techniques, several new sufficient conditions guaranteeing the mean square exponential stability of its equilibrium solution are obtained. The derived results are less conservative than the results recently presented in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008). In fact, the systems discussed in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008) are special cases of ours. Two examples are presented to illustrate the effectiveness and efficiency of the results.     

Global exponential stability of delayed reaction–diffusion neural networks with time-varying coefficients

In the current paper, a class of general neural networks with time-varying coefficients, reaction–diffusion terms, and general time delays is studied. Several sufficient conditions guaranteeing its global exponential stability and the existence of periodic solutions are obtained through analytic methods such as Lyapunov functional and Poincaré mapping. The obtained results assume no boundedness, monotonicity or differentiability of activation functions and can be applied within a broader range of neural networks. Among the presented conditions, some are independent of time delay and expressed in terms of system parameters, so easy to verify and of leading significance in applications. For illustration, an example is given.     

H∞ state estimation of generalised neural networks with interval time-varying delays

This paper focuses on studying the H_∞ state estimation of generalised neural networks with interval time-varying delays. The integral terms in the time derivative of the Lyapunov–Krasovskii functional are handled by the Jensen’s inequality, reciprocally convex combination approach and a new Wirtinger-based double integral inequality. A delay-dependent criterion is derived under which the estimation error system is globally asymptotically stable with H_∞ performance. The proposed conditions are represented by linear matrix inequalities. Optimal H_∞ norm bounds are obtained easily by solving convex problems in terms of linear matrix inequalities. The advantage of employing the proposed inequalities is illustrated by numerical examples.     

Exponential stability of impulsive high-order Hopfield-type neural networks with delays and reaction–diffusion

The problem of global exponential stability analysis of Impulsive high-order Hopfield-type neural networks with time-varying delays and reaction–diffusion terms has been investigated in this paper. Using the Lyapunov function method and M-matrix theory, we establish the global exponential stability of the neural networks with its estimated exponential convergence rate. As an illustration, a numerical example is given using the results.     

Multistability analysis for a general class of delayed Cohen–Grossberg neural networks

In this paper, by discussing parameter conditions based on properties of activation functions, we decompose state space into positively invariant sets and establish sufficient conditions for the existence of locally stable equilibria for delayed Cohen–Grossberg neural networks (CGNNs) through Cauchy convergence principle. Some new criteria are derived for ensuring equilibria (periodic orbits) to be locally or globally exponentially stable in any designated region. Finally, our results are demonstrated by four numerical simulations.     

Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays

In this paper, robust H_∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.     

New criteria for globally exponential stability of delayed Cohen–Grossberg neural network

This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.