Neutral-type Delay Research Articles

Adaptive Exponential State Estimation for Markovian Jumping Neural Networks with Multi-delays and Lévy Noises

This paper discusses the adaptive exponential state estimation problem of neutral-type neural networks with multi-delays and Levy noises. The M-matrix method being different from other methods, such as the LMIs method, has been applied to deal with the problem. According to the M-matrix method, some state estimation criteria for neural networks concerning neutral-type delays and no neutral-type delays are acquired to ensure the adaptive exponential estimation. Finally, a simulation example is offered to show the advantages of the theoretical results.

Improved delay-probability-dependent results for stochastic neural networks with randomly occurring uncertainties and multiple delays

This study seeks to address the delay-probability-dependent stability problem for a new class of stochastic neural networks with randomly occurring uncertainties, neutral type delay, distributed delay and probability-distribution delay. The system not only includes the randomly occurring uncertainties of parameters (ROUPs) but also contains stochastic disturbances, which is not yet investigated in existing papers. First, several stochastic variables which obey Bernoulli distribution are introduced to describe the ROUPs, based on which a new model is built. Second, through fully considering the information on kinds of delays and utilising general delay-partitioning method, an improved Lyapunov–Krasovskii function (LKF) is constructed. Combining Itô's differential formula, general bounding, free-weighting matrix and stochastic methods, a new delay-probability-dependent robustly mean square stable criterion is formulated in terms of linear matrix inequality. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.

Almost periodic cellular neural networks with neutral-type proportional delays

ABSTRACTThis paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.

Global convergence of CNNs with neutral type delays and D operator

A model of cellular neural networks with neutral type delays and D operator is proposed. Applying appropriate differential inequality techniques, several sufficient conditions are derived to ensure...

New robustness bounds for neutral type delay systems via functionals with prescribed derivative

The paper is devoted to the robust stability analysis of linear neutral type time delay systems with a constant delay and norm-bounded uncertainties. The method is based on the Lyapunov–Krasovskii functional with a derivative prescribed as a negative definite quadratic form of the “current” system state, which is considered to be not suitable for the robustness analysis due to the fact that it does not admit a quadratic lower bound. Unlike existing results, our approach does not require the derivative of the functional along the solutions of the perturbed system to be negative definite. Instead, we need just an essential part of the integral of the derivative to be negative. The resulting stability condition is presented in the form of a simple inequality depending on the so-called Lyapunov matrix, under an assumption that the difference operator of the perturbed system is stable. The result is applicable to all exponentially stable systems.

Computation of the region of attraction for a class of nonlinear neutral type delay systems

An estimation of the region of attraction of the trivial solution of nonlinear neutral type delay systems is presented by using the so called Lyapunov-Krasovskii functionals of complete type. Results concerning bounds on the delay Lyapunov matrix allow simplifying computations in the estimation of this region. The result is illustrated by some examples.

Global dissipativity of memristor-based neutral type inertial neural networks

The problem of global dissipativity for memristor-based inertial networks with time-varying delay of neutral type is investigated in this paper. Based on a proper variable substitution, the inertial system is transformed into a conventional system. Some sufficient criteria are established to ascertain the global dissipativity for the aforementioned inertial neural networks by employing analytical techniques and Lyapunov method. Meanwhile, the globally exponentially attractive sets and positive invariant sets are also presented here. Finally, numerical examples and simulations are given out to corroborate the effectiveness of obtained results.

Exponential decay for a neutral one-dimensional viscoelastic equation

In this work we consider a viscoelastic string subject to a delay of neutral type. The delay occurs in the second time derivative. Although delays are known by their destructive nature, here we prove an exponential decay result. We shall use the multiplier method and modify the classical energy by judicious choices of other functionals. This would lead to an appropriate differential inequality which allows us to conclude. It seems that this issue has never been discussed before in the literature.

EXPONENTIAL DECAY FOR A NEUTRAL WAVE EQUATION

A strongly damped wave equation involving a delay of neutral type in its second order derivative is considered. It is proved that solutions decay to zero exponentially despite the fact that delays are, in general, sources of instability

Global convergence of CNNs with neutral type delays and D operator

A model of cellular neural networks with neutral type delays and D operator is proposed. Applying appropriate differential inequality techniques, several sufficient conditions are derived to ensure the global exponential convergence of solutions for the proposed neural networks. Finally, a numerical simulation example is given to illustrate the effectiveness of the obtained results.

Obtention of the functional of complete type for neutral type delay systems via a new Cauchy formula

In this paper, we present a new manner for computing the so-called new form of the functional of complete type for neutral type time-delay systems without assumptions of continuity and differentiability on the initial function. It is obtained by using a new Cauchy formula. We present briefly the necessary stability conditions depending on the delay Lyapunov matrix that this result makes possible to prove.

Stability analysis of two-dimensional neutral-type Cohen–Grossberg BAM neural networks

Two-dimensional system model represents a wide range of practical systems, such as image data processing and transmission, thermal processes, gas absorption and water stream heating. Moreover, there are few dynamical discussions for the two-dimensional neutral-type Cohen–Grossberg BAM neural networks. Hence, in this paper, our purpose is to investigate the stability of two-dimensional neutral-type Cohen–Grossberg BAM neural networks. The first objective is to construct mathematical models to illustrate the two-dimensional structure and the neutral-type delays in Cohen–Grossberg BAM neural networks. Then, a sufficient condition is given to achieve the stability of two-dimensional neutral-type continuous Cohen–Grossberg BAM neural networks. Finally, simulation results are given to illustrate the usefulness of the developed criteria.

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.

Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays

In this paper, we consider exponential stability problem for neutral-type neural networks with both interval time-varying state and neutral-type delays under more generalized activation functions. We note that discrete and neutral delays are both time-varying where the discrete delay is not necessarily differentiable and the information on derivative of neutral delay is not required. To the best of our knowledge, this is the first study under this conditions on discrete and neutral delays. Furthermore, we consider the case when there are interconnections between past state derivatives, namely, neural networks contain activation function of past state derivatives. Based on the Lyapunov–Krasovskii functional, we derive new delay-dependent exponential stability criteria in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Finally, numerical examples are given to illustrate the effectiveness of theoretical results and to show less conservativeness than some existing results in the literature.

Almost sure exponential stability of stochastic Cohen–Grossberg neural networks with continuous distributed delays of neutral type

In this paper, a class of stochastic Cohen–Grossberg neural networks (SCGNNS) with continuous distributed delays of neutral type is considered. Firstly, some conditions are derived to ensure the existence and uniqueness of the almost periodic solution by means of contraction mapping principle and inequality techniques. Then by employing the nonnegative semi-martingale convergence theorem, the almost sure exponential stability of the SCGNNS is investigated, and some new results are established. Finally, one example is given to illustrate the obtained results.

Stochastic sampled-data H∞ synchronization of coupled neutral-type delay partial differential systems

This paper discusses the asymptotical synchronization and H∞ synchronization of coupled neutral-type delay partial differential systems (NDPDSs). A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. By using the method of a nonsingular matrix transformation, we decouple the coupled error dynamical systems. Then, sufficient conditions that guarantee the asymptotic stability of decoupled synchronization error dynamical systems are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and by using Jensen׳s inequality and reciprocally convex combination technique, which implies the asymptotical synchronization of the coupled NDPDSs. Moreover, the stability criteria for the H∞ stabilization of decoupled synchronization error dynamical systems with external disturbances are also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled NDPDSs. The equivalence between the H∞ stability of decoupled synchronization error dynamical systems and the H∞ synchronization of coupled NDPDSs is also proved by mathematical analysis. Finally, numerical examples are provided to demonstrate the effectiveness of the obtained results.

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

This paper considers the asymptotical synchronization and $$H_\infty $$H? synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov---Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the $$H_\infty $$H? synchronization problem is also considered. The equivalence between the $$H_\infty $$H? stability of decoupled synchronization error dynamical systems and the $$H_\infty $$H? synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the $$H_\infty $$H? stabilization is presented, which guarantees the $$H_\infty $$H? synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.

Stability Analysis of Time-Varying Neutral Time-Delay Systems

We propose a new technique of stability analysis for a general family of linear time-varying systems with delay of neutral type. We establish results of exponential stability through a new technique which relies on the notion of nonnegative system and the design of linear time-varying Lyapunov functionals. However, the studied systems are not assumed to be nonnegative.

New approach to periodicity of neutral type delay difference equations

New approach to periodicity of neutral type delay difference equations

Computational method for singularly perturbed delay differential equations with twin layers or oscillatory behaviour

In this paper, we have presented a computational method for solving singularly perturbed delay differential equations with twin layers or oscillatory behaviour. In this method, the original second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, we have employed numerical integration and linear interpolation to get tridiagonal system. This tridiagonal system is solved efficiently by using discrete invariant imbedding algorithm. Several model examples are solved, and computational results are presented by taking various values of the delay parameter and perturbation parameter. We have also discussed the convergence of the method.