Leakage Time-varying Delays Research Articles

Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales

In this paper, by using a continuation theorem of coincidence degree theory and differential inequality techniques, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of BAM neural networks with time-varying leakage delays and impulses on time scales. In addition, we present an illustrative example to show the feasibility of obtained results.

New results on the stability of fuzzy cellular neural networks with time-varying leakage delays

In this paper, fuzzy cellular neural networks with time-varying delays in the leakage terms are studied. Without assuming the boundedness on the activation functions, some sufficient conditions for the existence, uniqueness and global exponential stability of equilibrium point are established by using the fixed point theorem and constructing suitable Lyapunov functional, which are new, and they improve previously known results. Moreover, an example is given to demonstrate the feasibility of our method.

New results on almost periodic solutions for CNNs with time-varying leakage delays

In this paper, based on the exponential dichotomy theory and contraction mapping fixed point theorem, we obtain some sufficient conditions ensuring the global exponential stability of almost periodic solutions for a new generalized cellular neural network model with time-varying delays in leakage (or forgetting) terms. Our results complement some recent ones. Moreover, an illustrative example and its numerical simulation are given to demonstrate the effectiveness of the obtained results.

Exponential stability of FCNNs with time-varying leakage delays and reaction–diffusion terms

Abstract In this paper, we investigate the global exponential stability of fuzzy cellular neural networks with time-varying delays in the leakage terms and reaction–diffusion terms. By constructing a novel Lyapunov functional and applying inequality technique, we obtain some new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium solution. Moreover, an numerical example is provided to demonstrate the feasibility of our method.

Comments on “Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach”

Comments on “Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach”

Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays

In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov–Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.

Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control

This paper deals with the globally exponential stability of impulsive bidirectional associative memory (BAM) neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are determined by a continuous-time, discrete-state Markov chain. Different from the previous literature, the mixed time delays considered here comprise discrete, distributed and leakage time-varying delays. By using the Lyapunov–Krasovskii functional having triple integral terms and model transformation technique, some novel sufficient delay-dependent conditions are derived to ensure the globally exponential stability in the mean square of the suggested system. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the theoretical results.

The exponential stability of BAM neural networks with leakage time-varying delays and sampled-data state feedback input

Abstract In this paper, the exponential stability of bidirectional associative memory neural networks with leakage time-varying delays and sampled-data state feedback input is considered. By applying the time-delay approach, some conditions for ensuring the stability of a system are obtained. In addition, a numerical example is given to demonstrate the effectiveness of the obtained results.

Robust Exponential Stability of Impulsive Stochastic Neural Networks with Leakage Time-Varying Delay

This paper investigates mean-square robust exponential stability of the equilibrium point of stochastic neural networks with leakage time-varying delays and impulsive perturbations. By using Lyapunov functions and Razumikhin techniques, some easy-to-test criteria of the stability are derived. Two examples are provided to illustrate the efficiency of the results.

Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNNs with Time-Varying Leakage Delays

This paper is concerned with the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays in the leakage (or forgetting) terms. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of pseudo almost periodic solutions by using Lyapunov functional method and differential inequality techniques. We also provide numerical simulations to support the theoretical result.

Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.

Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays

This paper presents a new generalized cellular neural network model with time-varying delays in leakage (or forgetting) terms. By using Lyapunov functional method and differential inequality techniques, we obtain some sufficient conditions ensuring the existence and exponential stability of almost periodic solutions for the considered model. Our results complement with some recent ones. Moreover, an illustrative example is given to demonstrate the effectiveness of the obtained results.

Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays

This paper is concerned with a class of high-order cellular neural networks (HCNNs) model with time-varying delays in the leakage terms. By using the Lyapunov functional method and differential inequality techniques, we establish sufficient conditions on the existence and exponential stability of anti-periodic solutions for the model. Our results complement some recent ones. MSC:34C25, 34D40.

Effects of leakage time-varying delays in Markovian jump neural networks with impulse control

In this paper, the stability analysis problem is investigated for delayed neural networks with mixed time-varying delays, impulsive control and Markovian jumping parameters. The mixed time-varying delays include leakage, discrete and distributed time-varying delays. Sufficient conditions for the global exponential stability in the mean square are derived by using Lyapunov–Krasovskii functional having triple integral terms and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical softwares. Finally, three numerical examples and simulations are given to demonstrate the usefulness and effectiveness of the presented results.

Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

This paper first points out some fatal errors in the paper (Nonlinear Dyn 73:1367–1383, 2013). Then the main results of the above paper are corrected with some suitable modifications. The new feedback gain matrix is used to prove the estimation of the neuron states through numerical simulations with the same examples as discussed in the above paper.

Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

State Estimation for Neural Networks with Leakage Delay and Time-Varying Delays

The state estimation problem is investigated for neural networks with leakage delay and time-varying delay as well as for general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality techniques, a delay-dependent linear matrix inequalities (LMIs) condition is developed to estimate the neuron state with some observed output measurements such that the error-state system is globally asymptotically stable. An example is given to show the effectiveness of the proposed criterion.

Effect of leakage time-varying delay on stability of nonlinear differential systems

In this paper, a class of nonlinear differential systems with leakage time-varying delay is considered. Sufficient conditions for the existence-uniqueness and global asymptotic stability of the equilibrium point are derived by using fixed point theorems, Lyapunov–Krasovskii functional and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of a linear matrix inequality (LMI), which can be efficiently solved via standard numerical software. Even for the case of leakage constant delay, the criterion is shown to be less conservative than a recent publication. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.