Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov-Krasovskii Functionals

Relaxed stability criteria of delayed neural networks using delay-parameters-dependent slack matrices

This note aims to reduce the conservatism of stability criteria for neural networks with time-varying delay. To this goal, on the one hand, we construct an augmented Lyapunov-Krasovskii functional (LKF), incorporating some delay-product terms that capture more information about neural states. On the other hand, when dealing with the derivative of the LKF, we introduce several parameter-dependent slack matrices into an affine integral inequality, zero equations, and the S-procedure. As a result, more relaxed stability criteria are obtained by employing the so-called Lyapunov-Krasovskii Theorem. Two numerical examples show that the proposed stability criteria are of less conservatism compared with some existing methods.

Improved Stability Analysis Results of Generalized Neural Networks With Time-Varying Delays

This article studies the stability problem of generalized neural networks (GNNs) with time-varying delay. The delay has two cases: the first case is that the delay's derivative has only upper bound, the other case has no information of its derivative or itself is not differentiable. For both two cases, we provide novel stability criteria based on novel Lyapunov-Krasovskii functionals (LKFs) and new negative definite conditions (NDCs) of matrix-valued cubic polynomials. In contrast with the existing methods, in this article, the proposed criteria do not need to introduce extra state variables, and the positive-definite constraint on the novel LKF is relaxed. Moreover, based on free-matrix-based inequality (FMBI) and new NDCs, the stability conditions are expressed as linear matrix inequalities (LMIs). Eventually, the merits and efficiency of the proposed criteria are checked through some classical numerical examples.

Hierarchical Passivity Criterion for Delayed Neural Networks via A General Delay-Product-Type Lyapunov-Krasovskii Functional

This article is concerned with passivity analysis of neural networks with a time-varying delay. Several techniques in the domain are improved to establish the new passivity criterion with less conservatism. First, a Lyapunov-Krasovskii functional (LKF) is constructed with two general delay-product-type terms which contain any chosen degree of polynomials in time-varying delay. Second, a general convexity lemma without conservatism is developed to address the positive-definiteness of the LKF and the negative-definiteness of its time-derivative. Then, with these improved results, a hierarchical passivity criterion of less conservatism is obtained for neural networks with a time-varying delay, whose size and conservatism vary with the maximal degree of the time-varying delay polynomial in the LKF. It is shown that the conservatism of the passivity criterion does not always reduce as the degree of the time-varying delay polynomial increases. Finally, a numerical example is given to illustrate the proposed criterion and benchmark against the existing results.

Input-to-State Stabilization of Stochastic Markovian Jump Systems Under Communication Constraints: Genetic Algorithm-Based Performance Optimization

This work investigates the stabilization problem of uncertain stochastic Markovian jump systems (MJSs) under communication constraints. To reduce the bandwidth usage, a discrete-time Markovian chain is employed to implement the stochastic communication protocol (SCP) scheduling of the sensor nodes, by which only one sensor node is chosen to access the network at each transmission instant. Moreover, due to the effect of amplitude attenuation, time delay, and random interference/noise, the transmission may be inevitably subject to the Rice fading phenomenon. All of these constraints make the controller only receive the fading signal from one activated sensor node at each instant. A merge approach is first used to deal with two Markovian chains; meanwhile, a compensator is designed to provide available information for the controller. By a compensator and mode-based sliding-mode controller, the resulting closed-loop system is ensured to be input-to-state stable in probability (ISSiP), and the quasisliding mode is attained. Moreover, an iteration optimizing algorithm is provided to reduce the convergence domain around the sliding surface via searching a desirable sliding gain, which constitutes an effective GA-based sliding-mode control strategy. Finally, the proposed control scheme is verified via the simulation results.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Stability Analysis for Delayed Neural Networks via a Novel Negative-Definiteness Determination Method

The stability of neural networks with a time-varying delay is studied in this article. First, a relaxed Lyapunov-Krasovskii functional (LKF) is presented, in which the positive-definiteness requirement of the augmented quadratic term and the delay-product-type terms are set free, and two double integral states are augmented into the single integral terms at the same time. Second, a new negative-definiteness determination method is put forward for quadratic functions by utilizing Taylor's formula and the interval-decomposition approach. This method encompasses the previous negative-definiteness determination approaches and has less conservatism. Finally, the proposed LKF and the negative-definiteness determination method are applied to the stability analysis of neural networks with a time-varying delay, whose advantages are shown by two numerical examples.

Improved Stability Criteria for Delayed Neural Networks Using a Quadratic Function Negative-Definiteness Approach

This brief is concerned with the stability of a neural network with a time-varying delay using the quadratic function negative-definiteness approach reported recently. A more general reciprocally convex combination inequality is taken to introduce some quadratic terms into the time derivative of a Lyapunov-Krasovskii (L-K) functional. As a result, the time derivative of the L-K functional is estimated by a novel quadratic function on the time-varying delay. Moreover, a simple way is introduced to calculate the coefficients of a quadratic function, which avoids tedious works by hand as done in some studies. The L-K functional approach is applied to derive a hierarchical type stability criterion for the delayed neural networks, which is of less conservatism in comparison with some existing results through two well-studied numerical examples.

H∞ State Estimation for Neural Networks With General Activation Function and Mixed Time-Varying Delays

This article deals with H_∞ state estimation of neural networks with mixed delays. In order to make full use of delay information, novel delay-product Lyapunov-Krasovskii functional (LKF) by using parameterized delay interval is first constructed. Then, generalized free-weighting-matrix integral inequality is used to estimate the derivative of LKF to reduce the conservatism. Also, a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model. Finally, sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed H_∞ performance. Numerical examples are simulated to show the benefits of our proposed method.

Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach

This article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time-varying delays. First, tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks. Second, a sufficient criterion for the existence, uniqueness, and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse-delay-dependent Lyapunov-Krasovskii functional method. It is worth emphasizing that the addressed Lyapunov-Krasovskii functional covers both triple integral terms and novel quadruple integral terms, which makes the conservatism of the above criteria decrease. Even if the original neural network models are unstable or the impulsive effects are strong, the addressed neural network model can produce a globally exponentially stable periodic solution. These results here, which include boundedness, globally uniformly exponential convergence, and globally exponentially stability of the periodic solution, generalize and improve the earlier publications. Finally, two numerical examples and their computer simulations are given to show the effectiveness of theoretical results.

Dynamic event-based state estimation for delayed artificial neural networks with multiplicative noises: A gain-scheduled approach

This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with multiplicative noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.

Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays

In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ-norm). A general DDD HNN model is firstly introduced, where the discrete delays τ_pq(t) are asynchronous time-varying delays. Then, {ξ,1}-norm, {ξ,2}-norm and {ξ,∞}-norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ-stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Distributed Training for Multi-Layer Neural Networks by Consensus

Over the past decade, there has been a growing interest in large-scale and privacy-concerned machine learning, especially in the situation where the data cannot be shared due to privacy protection or cannot be centralized due to computational limitations. Parallel computation has been proposed to circumvent these limitations, usually based on the master-slave and decentralized topologies, and the comparison study shows that a decentralized graph could avoid the possible communication jam on the central agent but incur extra communication cost. In this brief, a consensus algorithm is designed to allow all agents over the decentralized graph to converge to each other, and the distributed neural networks with enough consensus steps could have nearly the same performance as the centralized training model. Through the analysis of convergence, it is proved that all agents over an undirected graph could converge to the same optimal model even with only a single consensus step, and this can significantly reduce the communication cost. Simulation studies demonstrate that the proposed distributed training algorithm for multi-layer neural networks without data exchange could exhibit comparable or even better performance than the centralized training model.

Passivity Analysis of Delayed Neural Networks Based on Lyapunov-Krasovskii Functionals With Delay-Dependent Matrices

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

Stability Analysis for Delayed Neural Networks With an Improved General Free-Matrix-Based Integral Inequality

This paper revisits the problem of stability analysis for neural networks with a time-varying delay. An improved general free-matrix-based (FMB) integral inequality is proposed with an undetermined number m . Compared with the conventional FMB ones, the improved inequality involves a much smaller number of free matrix variables. In particular, the improved FMB integral inequality is expressed in a concrete form for any value of m . By employing the new inequality with a properly constructed Lyapunov-Krasovskii functional, a new stability condition is derived for neural networks with a time-varying delay. Two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens.

Further Results on Adaptive Stabilization of High-Order Stochastic Nonlinear Systems Subject to Uncertainties

This paper concerns the adaptive state-feedback control for a class of high-order stochastic nonlinear systems with uncertainties including time-varying delay, unknown control gain, and parameter perturbation. The commonly used growth assumptions on system nonlinearities are removed, and the adaptive control technique is combined with the sign function to deal with the unknown control gain. Then, with the help of the radial basis function neural network approximation approach and Lyapunov-Krasovskii functional, an adaptive state-feedback controller is obtained through the backstepping design procedure. It is verified that the constructed controller can render the closed-loop system semiglobally uniformly ultimately bounded. Finally, both the practical and numerical examples are presented to validate the effectiveness of the proposed scheme.

Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

Reliable mixed H∞ and passive control for networked control systems under adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations

In this paper, the problem of reliable mixed H_∞ and passive control for a class of nonlinear networked control systems under the adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations is studied. Firstly, a series of independent stochastic variables with certain probabilistic distribution are presented to formulate the phenomena of actuator faults. Then, different from the traditional event-triggered scheme, the threshold of adaptive event-triggered scheme is determined by an online adaptive control law instead of the preset constant value. Further, based on a novel Lyapunov functional by taking the adaptive control law into account, sufficient conditions for asymptotically stable with mixed H_∞ and passive performance are obtained in terms of a set of LMIs. If these LMIs are feasible, the reliable mixed H_∞ and passive control gain and the weight parameter of adaptive event-triggered scheme can be gained simultaneously. Finally, two numerical examples are provided to show the effectiveness of the developed technique.

A New Approach to Stochastic Stability of Markovian Neural Networks With Generalized Transition Rates

This paper investigates the stability problem of Markovian neural networks (MNNs) with time delay. First, to reflect more realistic behaviors, more generalized transition rates are considered for MNNs, where all transition rates of some jumping modes are completely unknown. Second, a new approach, namely time-delay-dependent-matrix (TDDM) approach, is proposed for the first time. The TDDM approach is associated with both time delay and its time derivative. Thus, the TDDM approach can fully capture the information of time delay and would play a key role in deriving less conservative results. Third, based on the TDDM approach and applying Wirtinger's inequality and improved reciprocally convex inequality, stability criteria are derived. In comparison with some existing results, our results are not only less conservative but also involve lower calculation complexity. Finally, numerical examples are provided to show the effectiveness and advantages of the proposed results.

Hierarchical Stability Conditions for a Class of Generalized Neural Networks With Multiple Discrete and Distributed Delays

This brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays. To tackle delays arising in different neuron activation functions, we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks. We then generalize the Bessel-Legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states. Based on these inequalities, we design the Lyapunov-Krasovskii functional and derive hierarchical linear matrix inequality stability conditions. Finally, three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results.

Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays

This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov-Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov-Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.

Improved delay-dependent stability result for neural networks with time-varying delays

This paper is concerned with a new Lyapunov-Krasovskii functional (LKF) approach to the stability for neural networks with time-varying delays. The LKF has two features: First, it can make full use of the information of the activation function. Second, it employs the information of the maximal delayed state as well as the instant state and the delayed state. When estimating the derivative of the LKF we employ a new technique that has two characteristics: One is that Wirtinger-based integral inequality and an extended reciprocally convex inequality are jointly employed; the other is that the information of the activation function is used as much as we can. Based on Lyapunov stability theory, a new stability result is obtained. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.

Extended dissipative filter design for T-S fuzzy systems with multiple time delays

This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H_∞, L₂ - L_∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H_∞, L₂ - L_∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks

This paper deals with the global exponential stability for delayed recurrent neural networks (DRNNs). By constructing an augmented Lyapunov-Krasovskii functional and adopting the reciprocally convex combination approach and Wirtinger-based integral inequality, delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities. Meanwhile, a general and effective method on global exponential stability analysis for DRNNs is given through a lemma, where the exponential convergence rate can be estimated. With this lemma, some global asymptotic stability criteria of DRNNs acquired in previous studies can be generalized to global exponential stability ones. Finally, a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results.

Stability of Recurrent Neural Networks With Time-Varying Delay via Flexible Terminal Method

This brief is concerned with the stability criteria for recurrent neural networks with time-varying delay. First, based on convex combination technique, a delay interval with fixed terminals is changed into the one with flexible terminals, which is called flexible terminal method (FTM). Second, based on the FTM, a novel Lyapunov-Krasovskii functional is constructed, in which the integral interval associated with delayed variables is not fixed. Thus, the FTM can achieve the same effect as that of delay-partitioning method, while their implementary ways are different. Guided by FTM, Wirtinger-based integral inequality and free-weight matrix method are employed to develop several stability criteria, respectively. Finally, the feasibility and the effectiveness of the proposed results are tested by two numerical examples.

On Stabilization of Quantized Sampled-Data Neural-Network-Based Control Systems

This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.

Further triple integral approach to mixed-delay-dependent stability of time-delay neutral systems

This paper studies the asymptotic stability for a class of neutral systems with mixed time-varying delays. Through utilizing some Wirtinger-based integral inequalities and extending the convex combination technique, the upper bound on derivative of Lyapunov-Krasovskii (L-K) functional can be estimated more tightly and three mixed-delay-dependent criteria are proposed in terms of linear matrix inequalities (LMIs), in which the nonlinearity and parameter uncertainties are also involved, respectively. Different from those existent works, based on the interconnected relationship between neutral delay and state one, some novel triple integral functional terms are constructed and the conservatism can be effectively reduced. Finally, two numerical examples are given to show the benefits of the proposed criteria.

Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities

This paper investigates the issue of finite-time state estimation for coupled Markovian neural networks subject to sensor nonlinearities, where the Markov chain with partially unknown transition probabilities is considered. A Luenberger-type state estimator is proposed based on incomplete measurements, and the estimation error system is derived by using the Kronecker product. By using the Lyapunov method, sufficient conditions are established, which guarantee that the estimation error system is stochastically finite-time bounded and stochastically finite-time stable, respectively. Then, the estimator gains are obtained via solving a set of coupled linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design method.

Complete stability of delayed recurrent neural networks with Gaussian activation functions

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3^k equilibrium points with 0≤k≤n, among which 2^k and 3^k-2^k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results.