Leakage Delay Research Articles

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen’s inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays

Abstract In this paper, the problems of dissipativity and passivity analysis for memristor-based neural networks (MNNs) with both time-varying leakage delay and two additive time-varying delays are studied. By introducing an improved Lyapunov–Krasovskii functional (LKF) with triple integral terms, and combining the reciprocally convex combination technique, Wirtinger-based integral inequality with free-weighting matrices technique, some less conservative delay-dependent dissipativity and passivity criteria are obtained. The proposed criteria that depend on the upper bounds of the leakage and additive time-varying delays are given in terms of linear matrix inequalities (LMI), which can be solved by MATLAB LMI Control Toolbox. Meanwhile, the criteria for the system with a single time-varying delay are also provided. Finally, some examples are given to illustrate the effectiveness and superiority of the obtained results.

Global dissipativity analysis for memristor-based uncertain neural networks with time delay in the leakage term

This paper is concerned with the problem of global dissipativity analysis for a class of memristor-based uncertain neural networks with leakage delay and state-dependent switched memductance functions. By combining differential inclusions with set-valued maps and constructing a proper Lyapunov-Krasovskii functional, delaydependent criteria in terms of linear matrix inequalities are obtained for the global dissipativity of the memristive uncertain neural networks. Finally, a numerical example is given to illustrate the feasibility of the theoretical results.

Impulsive discrete-time GRNs with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue

Impulsive discrete-time GRNs with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue

Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control

In this paper, the global asymptotic stability of memristive bidirectional associative memory neural networks with leakage delay and two additive time-varying delays is firstly studied. Then, we propose a novel sampled-data feedback controller to guarantee the synchronization of system based on drive/response concept. In particular, taking full advantage of the input delay approach, the Lyapunov function method and the Jensen’s inequality theory, several sufficient conditions are obtained. Finally, two numerical simulation examples show the effectiveness of the designed sampled-data control strategy. Furthermore, our results can be applied to simulate the associative memory function of brain-like robots, large-scale information storage, etc.

Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay

The objective of this paper is to analyze the stability analysis of neutral-type neural networks with additive time-varying delay and leakage delay. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple and four integral terms, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. More information of the lower and upper delay bounds of time-varying delays are used to derive the stability criteria, which can lead less conservative results. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasible can be checked easily by MATLAB LMI control toolbox. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales

In this paper, by applying the exponential dichotomy theory on time scales, Banach contraction mapping principle and differential inequality analysis techniques, we establish some sufficient conditions for the existence and global exponential stability of almost automorphic solution for neutral type high-order Hopfield bidirectional associative memory (BAM) neural networks with time-varying leakage delays on time scales. In the addressed system, we not only consider the effects of the first-order neutral terms on networks, but also investigate the influences of the second-order neutral terms on the networks. High-order Hopfield BAM neural networks with continuously distributed leakage delays on time scales are also considered. Our results are completely new even if time scale T=R or T=Z and complementary to the previously existing results. Finally, three examples with numerical simulations are presented to illustrate the feasibility of our proposed theoretical results.

Improved criteria of delay-dependent stability for discrete-time neural networks with leakage delay

This paper is concerned with the stability analysis of discrete-time neural networks with leakage and time-varying delays. By a novel summation inequality, the technique of reciprocally convex combination and triple Lyapunov–Krasovskii terms, the various cases of time-delay are discussed in detail and improved criteria are established to ensure the delay-dependent stability of discrete-time neural networks. Finally, three examples are given to verify the effectiveness of the proposed methods.

New bifurcation results for fractional BAM neural network with leakage delay

Recently, the dynamics of the fractional delayed neural networks has been considerably concerned. It is illustrated that time delay has a remarkable influence on the dynamical behaviors of the fractional neural networks. Nevertheless, the results of the fractional neural network with leakage delay are extremely few. It is the first time that the stability and bifurcation of fractional BAM neural networks with time delay in leakage terms is examined in the current paper. The stability criterion and the conditions of bifurcation are obtained for the proposed systems with or without leakage delay by selecting time delay as the bifurcation parameter. It is amazing that the leakage delay has a destabilizing influence on the stability performance of such system and they cannot be ignored. Moreover, the relation between the bifurcation point and the order is fully discussed by careful calculation. Finally, numerical examples are addressed to verify the feasibility of the obtained theoretical results.

Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties

This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Global Exponential Convergence of Fuzzy Cellular Neural Networks with Leakage Delays, Distributed Delays and Proportional Delays

In this paper, a class of fuzzy cellular neural networks (FCNNs) with leakage delays, distributed delays and proportional delays are considered. Using the differential inequality strategy, some sufficient criteria which ensure the global exponential convergence of the FCNNs with leakage delays, distributed delays and proportional delays are established. Numerical simulations are given to explain the obtained analytical results. The derived conclusions of this article are new and complement some earlier publications.

Pseudo-Almost Periodic Solution on Time-Space Scales for a Novel Class of Competitive Neutral-Type Neural Networks with Mixed Time-Varying Delays and Leakage Delays

A competitive neural network model was proposed to describe the dynamics of cortical maps in which, there exist two memories: long-term and short-term. In this paper, we investigate the existence and the exponential stability of the pseudo-almost periodic solution of a system of equations modeling the dynamics of neutral-type competitive neural networks with mixed delays in the time-space scales for the first time. The mixed delays include time-varying delays and continuously distributed ones. Based on contraction principle and the theory of calculus on time-space scales, some new criteria proving the convergence of all solutions of the networks toward the unique pseudo-almost periodic solution are derived by using the ad-hoc Lyapunov–Krasovskii functional. Finally, numerical example with graphical illustration is given to confirm our main results.

Further results on dissipativity analysis for Markovian jump neural networks with randomly occurring uncertainties and leakage delays

This paper is concerned with the mixed $$H_\infty$$ and dissipativity performance for Markovian jump neural networks with time delay in the leakage term and randomly occurring uncertainties. The randomly occurring uncertainties are assumed to be mutually uncorrelated Bernoulli-distributed white noise sequences. By introducing a triple-integrable term in the Lyapunov functional, the Wirtinger-based double-integral inequality is utilized to bound the derivative of the triple-integral term and then a sufficient condition is derived to ensure that the considered neural networks to be strict $$({\mathcal {Q,S,R}}) - \gamma$$ -dissipative and passive. These conditions are presented in terms of linear matrix inequalities, which can be easily solved by using standard numerical software. Finally, numerical examples are given to show the effectiveness and the potential significance of the proposed results.

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.

Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays

This paper discusses the stability in Lagrange sense for complex-valued neural networks with time-varying discrete delays and distributed delays as well as leakage delay. By constructing an appropriate Lyapunov–Krasovskii functional, and employing free-weighting-matrix approach and inequality techniques in matrix form, a sufficient criterion to guarantee global exponential stability in Lagrange sense is obtained for the investigated neural networks. The given criterion is delay-dependent and is shown as linear matrix inequalities in complex domain, which can be calculated numerically applying valid YALMIP toolbox in MATLAB. A numerical example is provided to manifest the validity of the proposed result.

Effects of leakage delays and impulsive control in dissipativity analysis of Takagi–Sugeno fuzzy neural networks with randomly occurring uncertainties

In this paper, dissipativity analysis problem is investigated for T-S fuzzy neural networks with leakage delays and impulsive effects. Sufficient conditions for the dissipativity criteria are derived by using Lyapunov–Krasovskii functional having triple and four integral terms with free weighting matrix method. The obtained results are dependent on the the leakage delay and upper bound of time-varying delay. Moreover, some comparisons are made to contrast to some of existing results about strictly (Q,S,R)−ϑ-dissipativity for the concerned neural networks. Finally, some numerical examples and their computer simulations are given to show the effectiveness of the proposed criteria.

The Sampled-data Exponential Stability of BAM with Distributed Leakage Delays

This paper investigates the exponential stability of bidirectional associative memory (BAM) neural networks with distributed leakage delays and sampled-data state feedback input. Based on the input delay approach, the considered BAM neural networks is transformed into a system with mixed distributed leakage delays and time-varying discrete delays. Some sufficient conditions are given to ensure that the system is exponentially stable. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

Delay-Dependent Passivity and Stability Analysis for a Class of Memristor-Based Neural Networks with Time Delay in the Leakage Term

This paper is concerned with the problem of passivity and stability analysis for a class of memristor-based neural networks with leakage delay and state-dependent switched memductance functions. By combining differential inclusions with set-valued maps and constructing a proper Lyapunov–Krasovskii functional, delay-dependent criteria in terms of linear matrix inequalities are obtained for the passivity of the memristive neural networks. Meanwhile, based on the derived criteria, stability criteria are obtained for the networks via Barbalat’s lemma. Finally, a numerical example is given to illustrate the feasibility of the theoretical results.

Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays

This paper is concerned with a class of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee that all solutions of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays converge exponentially to zero vector are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

ABSTRACTThis paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.