Leakage Delay Research Articles

Sliding Mode Stabilization of Memristive Neural Networks With Leakage Delays and Control Disturbance.

In this article, we investigate a class of memristive neural networks (MNNs) with time-varying delays and leakage delays via sliding mode control (SMC) with and without control disturbance. SMC is used to ensure MNNs' stability. According to the characteristics of the MNNs, we consider the following three models: the first is the MNNs with time-varying delays, the second is the MNNs with time-varying delays and the control disturbance, and the third is the MNNs with time-varying delays, leakage delays, and the control disturbance. We quote some assumptions and lemmas to ensure that our main results are true. The sliding surface, the corresponding sliding mode controller, and the Lyapunov functions are constructed in different models to ensure MNNs' stability. Finally, some examples and simulations verify the validity of our main results by solving linear matrix inequality (LMI), and the conclusions and analysis of the results are given.

Dissipativity of impulsive matrix-valued neural networks with leakage delay and mixed delays

A generalization of real-, complex-, and quaternion-valued neural networks is represented by matrix-valued neural networks (MVNNs), for which the states and weights are matrices. The dissipativity of impulsive MVNNs with leakage delay and mixed delays is studied in this paper, by giving sufficient criteria expressed in terms of real-valued linear matrix inequalities. After decomposing the MVNNs into real-valued systems, Lyapunov–Krasovskii functionals with double, triple, and quadruple integral terms are formulated. Also, the free weighting matrix method, simple, double, and triple Jensen inequalities, the reciprocally convex combination inequality, and the Wirtiger-based integral inequality are used to establish the sufficient criteria. Two numerical examples illustrate the feasibility and correctness of the proposed theoretical results.

Almost periodic solutions of quaternion-valued neutral type high-order Hopfield neural networks with state-dependent delays and leakage delays

In this paper, we consider the existence and global exponential stability of almost periodic solutions for a class of quaternion-valued neutral type neural networks with state-dependent delays and leakage delays by a direct approach. That is, without decomposing the considered quaternion-valued systems into real-valued systems, by using the contraction mapping fixed point theorem, we obtain the existence of almost periodic solutions of the considered networks with state-dependent delays and leakage delays, and by the counter-evidence method, we obtain the global exponential stability of almost periodic solutions of the considered networks with discrete delays and leakage delays. When the time delays in the considered systems are proportional time delays, our existence results are still true. At the same time, when the considered systems degenerate into real-valued or complex-valued systems, our results are still new.

Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay

In artificial neural networks, the diffusion phenomenon of electrons exists inevitably, due to the electromagnetic field of neural networks is heterogeneous. In this paper, we study the spatio-temporal dynamical behaviors of a reaction-diffusion neural network with leakage delay. By analyzing the corresponding characteristic equation, the sufficient and necessary conditions of Turing instability are obtained and the existence of Turing, Hopf, and Turing-Hopf bifurcations is also established. Furthermore, the truncated normal form up to third order is derived to understand and classify the spatio-temporal dynamics close to the Turing-Hopf bifurcation point. By numerical simulations, we find a pair of spatially inhomogeneous periodic solutions and illustrate the effects of time delays and spatial diffusion on the spatio-temporal dynamics of the model.

Joint influence of leakage delays and proportional delays on almost periodic solutions for FCNNs

This paper deals with fuzzy cellular neural networks (FCNNs) with leakage delays and proportional delays. Applying the differential inequality strategy, fixed point theorem and almost periodic function principle, some sufficient criteria which ensure the existence and global attractivity of a unique almost periodic solution for fuzzy cellular neuralnetworks with leakage delays and proportional delays are derived.Computer simulations are carried out to illustrate our theoreticalfindings. Our results are new and complement some previouspublished ones.

Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays

In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree theory and the Wirtinger inequality as well as constructing a suitable Lyapunov functional, sufficient conditions are derived to ensure the existence and global exponential stability of anti-periodic solutions via direct approaches. Our results are completely new. Finally, numerical examples are also provided to show the effectiveness of our results.

Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach

This paper investigates the global Mittag-Leffler synchronization (GMLS) issue for fractional-order delayed quaternion-valued neural networks, which include leakage delays and transmission delays. First, a new lemma is established to estimate the Caputo fractional derivative for quaternion self-conjugate quadratic Lyapunov function, and a novel quaternion-valued linear feedback controller is designed. Then by utilizing quaternion matrix theory and our proposed lemma, some succinct GMLS criteria are derived respectively in quaternion-valued linear matrix inequality (LMI) form and complex-valued LMI form, which simplify and extend some previous work on the synchronization control for quaternion-value neural networks. Finally, a numerical example is given to validate our theoretical results.

Lagrange stability for uncertain memristive neural networks with Lévy noise and leakage delay

In this paper, a class of uncertain memristive neural networks with leakage and time varying transmission delays as well as Lévy noise is studied. Based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals, the free-weighting matrix method and stochastic analysis technique, sufficient criteria in terms of linear matrix inequalities (LMIs) are given to ascertain the subsystems and memristive neural networks to be exponentially mean-square stable in Lagrange sense. Meanwhile the estimations of globally attractive sets are given. Finally, numerical examples are carried out to illustrate the feasibility of theoretical results.

Almost Automorphic Solutions to Cellular Neural Networks With Neutral Type Delays and Leakage Delays on Time Scales

In this paper, cellular neural networks (CNNs) with neutral type delays and time-varying leakage delays are investigated. By applying the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, a set of sufficient conditions which ensure the existence and exponential stability of almost automorphic solutions of the model are obtained. An example with its numerical simulations is given to support the theoretical findings.

Exponential Stability of Leakage Delay and Semi-Markovian Jump for Neutral-Type Neural Network

In this paper, a suitable Lyapunov-Krasovskii functional together with the inequality analysis technique for neutral-type system, and sufficient exponential stability conditions are proposed in the form of linear matrix inequalities (LMIs). Firstly, the system model of leakage delay and semi-Markovian process for neutral-type neural network is established, where the sojourn-time follows Weibull distribution, which is time-varying instead of being constant in the transition rate. Secondly, through combinations of stability analysis method, Lyapunov-Krasovskii functional and inequality analysis technique, some sufficient conditions have been achieved to undertake the exponential stabilization of given neural network system. Moreover, time delays of the system contain leakage and mixed delays, which are more general and appropriate. Finally, in order to show the many advantages of our model, the obtained results will be compared with previous works based on methods different from semi-Markovian jump or leakage delay.

Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays

Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays

Synchronization of semi-Markov coupled neural networks with impulse effects and leakage delay

This paper examines the robust synchronization problem for a class of coupled neural networks in mean-square sense subject to semi-Markov jump, outer coupling, leakage and time-varying delay through a resilient memory state feedback controller, wherein the effect of impulse strategy is considered in the system design. Particular, impulsive perturbation and leakage delay are incorporated in the system model cannot be neglected since they make huge impact on the stability behaviour. By endowing Lyapunov’s direct method, a newest set of necessary conditions is enhanced in the form of linear matrix inequalities (LMIs) which guarantee that the addressed system can realize synchronization criterion. Based on these obtained LMIs, the explicit characterization of the designed controller is retrieved interms of linear matrix inequalities by using the convex optimization algorithm. Eventually, the analytical design are voiced by a numerical example which substantiate the superiority and efficiency of the proposed control design strategy.

Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays. By utilizing the exponential dichotomy of linear differential equations, Banach’s fixed point theorem and differential inequality techniques, the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks. The results are completely new. Finally, the authors give an example to illustrate the feasibility of the results.

Exponential stability of discrete-time uncertain neural networks with multiple time-varying leakage delays

In this paper, we investigate a new exponential stability criterion for uncertain discrete-time neural networks with both multiple leakage time-varying delays and discrete time-varying delays. Here for the first time leakage time varying delay is taken to be a multiple one and this does not exist in the literature. Based on the discrete-type Halanay inequality and some inequality techniques, a novel exponential stability criterion for uncertain discrete-time neural networks is derived in terms of LMIs. Then the LMIs can be easily manipulated by using LMI Control toolbox in Matlab. Finally few numerical examples along with simulative responses are given to strengthen our proposed stability results.

Synchronization control of Markov jump neural networks with mixed time-varying delay and parameter uncertain based on sample point controller

This paper put forward an improved synchronization problem for neural networks with Markov jump parameters. The traditional Markov jump neural network (MJNN) only considers the basic external time-varying delays, ignoring both the distributed and leakage delays in the internal transmission of the neural network and the small time-varying errors in the mode switching of Markov probability transition rates. In this paper, we focus on the synchronization of MJNN with mixed time-varying delay. And an improved Lyapunov–Krasovskii functional is constructed. The convergence of inequalities is solved by using affine Bessel–Legendre inequalities and Wirtinger double integral inequalities. At the same time, a new method is used to optimize the mathematical geometric area of the time-varying delay and reduce the conservativeness of the system. Finally, a sample point controller is constructed to synchronize the driving system and the corresponding system.

Global µ-stability of neutral-type impulsive complex-valued BAM neural networks with leakage delay and unbounded time-varying delays

This paper investigates the existence and uniqueness of the equilibrium point and its global µ-stability for neutral-type impulsive complex-valued bidirectional associative memory neural networks with leakage delay and unbounded time-varying delays, by considering two types of Lipschitz conditions to be satisfied by the activation functions. The homeomorphism lemma is used to obtain a sufficient condition for the existence and uniqueness of the equilibrium point. Sufficient delay-dependent conditions both in terms of complex-valued and real-valued linear matrix inequalities which ensure the global µ-stability of the equilibrium point are obtained by constructing appropriate Lyapunov–Krasovskii functionals with simple, double, and triple integral terms, and using the free weighting matrix method, simple and double complex-valued Jensen inequalities, the complex-valued reciprocally convex combination inequality, and the complex-valued Wirtiger-based integral inequality. Lastly, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Finite-time boundedness of state estimation for semi-Markovian jump systems with distributed leakage delay and linear fractional uncertainties

ABSTRACTIn this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples.

Synchronization of memristive neural networks with leakage delay and parameters mismatch via event-triggered control

In this paper, we investigate the synchronization problem on delayed memristive neural networks (MNNs) with leakage delay and parameters mismatch via event-triggered control. We divide MNNs with parameters mismatch into two categories for discussion. One is state-dependent and can achieve synchronization by designing a suitable controller. A novel Lyapunov functional is constructed to analyze the synchronization problem. Moreover, the triggering conditions are independent from the delay boundaries and can be static or dynamic. Another category of parameters mismatch is structure-dependent and can only achieve quasi-synchronization by appropriate controller. By using matrix measure method and generalized Halanay inequality, a quasi-synchronization criterion is established. The controllers in this paper are discrete state-dependent and can be updated under the event-based triggering condition, which is more simpler than the previous results. In the end of our paper, two illustrative examples are given to support our results.

Synchronization of delayed coupled switched neural networks: Mode-dependent average impulsive interval

This paper investigates the synchronization of coupled switched neural networks with leakage delay and time-varying delay. The desynchronizing impulses and synchronizing impulses are taken into account in the constructed systems, and they are not required to act simultaneously with the switching behaviors. Moreover, a new concept named mode-dependent average impulsive interval is introduced. Based on Lyapunov functional method involving mode-dependent average dwell time method, the relation of time-delay, impulsive gains, system modes, mode-dependent average impulsive interval and mode-dependent average dwell time is established. Exponential synchronization criteria are presented for delayed switched neural networks with desynchronizing impulses and synchronizing impulses, respectively. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

Finite-Time Stabilization for Static Neural Networks with Leakage Delay and Time-Varying Delay

The problem of finite-time stabilization (FTS) for static neural networks (SNNs) with leakage delay and time-varying delay is investigated in this paper. By introducing an auxiliary function and utilizing the Lyapunov stability theory, we derive some sufficient criteria for FTS in terms of linear matrix inequalities (LMIs). Two feedback controllers are designed based on two different Lyapunov functions, which can be easily solved via MATLAB LMI toolbox, to guarantee the FTS for the SNNs. Finally, two numerical examples are given to illustrate the efficiency of our results.