Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

In this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.     

Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays

This paper investigates the global asymptotic stability problem for a class of neutral-type complex-valued neural networks with random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the information of time-varying delay is assumed to be random time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing inequality technique, several sufficient conditions are obtained to ensure the global asymptotically stability of equilibrium point for the considered neural networks. The obtained stability criterion is expressed in terms of complex-valued linear matrix inequalities, which can be simply solved by effective YALMIP toolbox in MATLAB. Finally, three numerical examples are given to demonstrate the efficiency of the proposed main results.     

Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered. A novel control method is given by using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks, and the estimation gains can also be obtained. Numerical examples are constructed to verify the theoretical analysis in this paper.     

Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays

The problem of delay-dependent stability analysis is investigated for discrete-time Markovian jump neural networks with mixed time-delays (both discrete and infinity-distributed time delays). The Markov chain in the underlying neural networks is finite piecewise homogeneous. A delay-dependent condition is derived for the addressed neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same type of neural networks but with partially known transition probabilities. Two numerical examples are given to demonstrate the usefulness of the derived methods.     

Neural networks and graph theory

The relationships between artificial neural networks and graph theory are considered in detail. The applications of artificial neural networks to many difficult problems of graph theory, especially NP-complete problems, and the applications of graph theory to artificial neural networks are discussed. For example graph theory is used to study the pattern classification problem on the discrete type feedforward neural networks, and the stability analysis of feedback artificial neural networks etc.     

Stability analysis based on partition trajectory approach for switched neural networks with fractional Brown noise disturbance

In this brief, the stability problem based on feedback control for two types of stochastic neural networks driven by fractional Brown noise is considered. One class is the switched neural networks without time delays and the other one is with time delays. A novel analysis method, very different to the usual approach based on the Itô formula and infinitesimal operator, is proposed in this paper. By the idea of splitting time of trajectory and associating with hölder inequality, some criteria are obtained to guarantee the switched neural networks with two types to be stable. In the end, two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results.     

Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.     

Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses

In this paper, the robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses is considered. It is assumed that the considered impulsive neural networks have norm-bounded parametric uncertainties and time-varying delays and the state variables on the impulses may relate to the time-varying delays. By using Lyapunov functions together with Razumikhin technique or with differential inequalities, some new robust exponential stability criteria are provided. Some examples and their simulations, including examples that the stability of which can not be tackled by the existing results, are also presented to illustrate the effectiveness and the advantage of the obtained results.     

Dynamic behavior of a class of neutral-type neural networks with discontinuous activations and time-varying delays

This paper is concerned with a class of neutral-type neural networks with discontinuous activations and time-varying delays. Under the concept of Filippov solution, by applying the differential inclusions and the topological degree theory in set-valued analysis, we employ a novel argument to establish new results on the existence of the periodic solutions for the considered neural networks. After that, we derive some criteria on the uniqueness, global exponential stability of the considered neural networks and convergence of the corresponding autonomous case of the considered neural networks, in terms of nonsmooth analysis theory with Lyapunov-like approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, the results obtained can also be valid. Our results extend previous works on the neutral-type neural networks to the discontinuous cases, some related results in the literature can be enriched and extended. Finally, two typical examples and the corresponding numerical simulations are provided to show the effectiveness and flexibility of the results derived in this paper.     

Stability analysis of dynamical neural networks

In this paper, we use the matrix measure technique to study the stability of dynamical neural networks. Testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given. It shows how a few well-known results can be unified and generalized in a straightforward way. Local exponential stability of a class of dynamical neural networks is also studied; we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks are obtained     

Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks

This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov–Krasovskii functional (LKF) method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.      

Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays

In this paper, a class of stochastic impulsive high-order BAM neural networks with time-varying delays is considered. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order BAM neural networks.     

Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

Exponential convergence and stability of delayed fuzzy cellular neural networks with time-varying coefficients

In this paper, the dynamic behaviors of fuzzy cellular neural networks (FCNNs) with time-varying coefficients and delays are considered. Some criteria are established to ensure the exponential convergence or exponential stability of such neural networks. The effectiveness of obtained results is illustrated by a numerical example.     

Stabilization of stochastic Hopfield neural network with distributed parameters

In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Ito formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Ito formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.     

Stochastic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters

In this paper, the global robust stability of uncertain recurrent neural networks with Markovian jumping parameters which are represented by the Takagi–Sugeno fuzzy model is considered. A novel linear matrix inequality-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in Arik [On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circ. Syst. I 47 (2000), pp. 571–574], Cao [Global stability conditions for delayed CNNs, IEEE Trans. Circ. Syst. I 48 (2001), pp. 1330–1333] and Lou and Cui [Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J. Math. Anal. Appl. 328 (2007), pp. 316–326] to show the effectiveness and conservativeness.     

Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory neural networks with mixed time-delays, where discrete, distributed and neutral delays are involved. By utilizing the delay decomposition approach and an appropriately constructed Lyapunov–Krasovskii functional, some novel delay-dependent and decay rate-dependent criteria for the exponential stability of the considered neural networks are derived and presented in terms of linear matrix inequalities. Furthermore, the maximum allowable decay rate can be estimated based on the obtained results. Three numerical examples are given to demonstrate the effectiveness of the proposed method.     

Finite-time stability on a class of SICNNs with neutral proportional delays

In this paper, the finite-time stability for a class of shunting inhibitory cellular neural networks with neutral proportional delays is discussed. By employing differential inequality techniques, several sufficient conditions are obtained to ensure the finite-time stability for the considered neural networks. Meanwhile, the generalized exponential synchronization is also established. An example along with its numerical simulation is presented to demonstrate the validity of the proposed results.

     

Exponential synchronization of a class of neural networks with time-varying delays.

This paper aims to present a synchronization scheme for a class of delayed neural networks, which covers the Hopfield neural networks and cellular neural networks with time-varying delays. A feedback control gain matrix is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory, and its exponential synchronization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Both the cellular neural networks and Hopfield neural networks with time-varying delays are given as examples for illustration.     

Stochastic Stability for a Class of Discrete-time Switched Neural Networks with Stochastic Noise and Time-varying Mixed Delays

In this paper, stochastic stability is analyzed for a class of discrete-time switched neural networks, in which time-varying mixed delays and stochastic noise are considered. Specifically, benefitting from the triple summation term included in a new Lyapunov functional, time-varying distributed delays are tackled and a criterion of decay estimation for a non-switched neural network is firstly obtained. Subsequently, in view of average dwell time methodology and stochastic analysis, several sufficient conditions are obtained to ensure that the stochastic stability problem is solvable. Furthermore, the derived sufficient conditions reflect that the decay rate of the considered neural networks has a close relationship with average dwell time, upper and lower bounds of delays and intensity of stochastic noise. Finally, validity of the inferred conclusions is given by a simulated example.