Delay-dependent exponential stability for a class of neural networks with time delays and reaction-diffusion terms

In this paper, the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays

This paper investigates the problem for stability of neutral-type dynamical neural networks involving delay parameters. Different form the previously reported results, the states of the neurons involve multiple delays and time derivative of states of neurons include discrete time delays. The stability of such neural systems has not been given much attention in the past literature due to the difficulty of finding Lyapunov functionals which are suitable for stability analysis of this type of neural networks. This paper constructs a generalized Lyapunov functional by introducing new terms into the well-known Lyapunov functional that enables us to conduct a theoretical investigation into stability analysis of delayed neutral-type neural systems. Based on this modified novel Lyapunov functional, sufficient criteria are derived, which guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of the neutral-type neural networks with multiple delays in the states and discrete delays in the time derivative of the states. The applicability of the proposed stability conditions rely on testing two basic matrix properties. The constraints impose on the system matrices are determined by using nonsingular M-matrix condition, and the constraints imposed on the coefficients of the time derivative of the delayed state variables are derived by exploiting the vector-matrix norms. We also note that the obtained stability conditions have no involvement with the delay parameters and expressed in terms of nonlinear Lipschitz activation functions. We present a constructive numerical example for this class of neural networks to give a systematic procedure for determining the imposed conditions on the whole system parameters of the delayed neutral-type neural systems.     

Further analysis of global robust stability of neural networks with multiple time delays

This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result.     

Robust mean square stability of delayed stochastic generalized uncertain impulsive reaction-diffusion neural networks

This article is dedicated to the investigation of the stability problem of delayed stochastic generalized uncertain impulsive reaction-diffusion neural networks (SGUIRDNNs). Applying Lyapunov second method, several new robust mean square stability criteria on the equilibrium point of the delayed SGUIRDNNs are derived in terms of linear matrix inequalities (LMIs). At last, we provide a numerical example to verify the validity of our findings.     

Parameter-dependent robust stability of uncertain neural networks with time-varying delay

This paper is concerned with the problem of global robust asymptotic stability for delayed neural networks with polytopic parameter uncertainties and time-varying delay. A delay-dependent and parameter-dependent robust stability criterion for the equilibrium of delayed neural networks in the face of polytopic type uncertainties is presented by using a parameter-dependent Lyapunov functional and taking the relationship between the terms in the Leibniz–Newton formula into account. This criterion, expressed as a set of linear matrix inequalities, requires no matrix variable to be fixed for the entire uncertainty polytope, which produces a less conservative stability result.     

Improved exponential stability analysis for delayed recurrent neural networks

In this paper, we investigate the problem of global exponential stability analysis for a class of delayed recurrent neural networks. This class includes Hopfield neural networks and cellular neural networks with interval time-delays. Improved exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed stability criteria are delay dependent and characterized by linear matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Novel stability criterion for cellular neural networks: An improved Gu's discretized LKF approach

Novel stability criterion is presented for the existence, uniqueness and globally asymptotic stability of the equilibrium point of a class of cellular neural networks with time-varying delays. Based on Gu's discretized Lyapunov–Krasovskii functional (LKF) theory, a novel vector LKF is introduced by dividing the variation interval of the time delay into several subintervals with equal length. By using the homeomorphism mapping principle, free-weighting matrix method and linear matrix inequality (LMI) techniques, the obtained condition is less conservative than some previous results. Three examples are also given to show the effectiveness of the presented criterion.     

An analysis of stability of neutral-type neural systems with constant time delays

This paper investigates the stability problem of a class of neutral-type neural networks with constant time delays. By constructing a proper Lyapunov functional, a novel sufficient condition for the global stability of the equilibrium point for the class of neutral-type neural systems is presented. The obtained stability condition is expressed in terms of the system parameters of the network, and therefore, it can be easily verified. We also give a comparative numerical example to show the applicability of the result and demonstrate its advantages over the previously published corresponding stability results.     

Input-to-state stability of impulsive inertial memristive neural networks with time-varying delayed

The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.     

Finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks

Without considering identical systems, this paper investigates the finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks (FDMNN) by designing a novel fractional sliding mode controller (SMC). Due to the existence of memristor, the research is under the framework of Filippov solution. We firstly construct a fractional integral sliding mode surface (SMS). Based on sliding mode control theory and Lyapunov stability theorem, a novel fractional SMC is proposed to realize the lag projective synchronization of nonidentical FDMNN in finite time, and the synchronization setting time is less conservative than the existing results. As the special cases, some sufficient conditions are extended to projective synchronization, lag synchronization, anti-lag synchronization of nonidentical FDMNN in finite time, which improve and enrich some existing results. At last, a simulation example is given to prove the validity of the conclusions.     

Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty

In this paper, we investigate the problem of finite-time stabilization of time-varying delayed neural networks with uncertainty. By employing the Lyapunov approach and linear matrix inequalities (LMIs), two different memory controllers are derived to achieve the finite-time stabilization of the addressed neural networks. Moreover, the upper bound of the setting-time for stabilization can be estimated via different Lyapunov functions. Our results improve and extend some recent works. Finally, the effectiveness and feasibility of the proposed controllers are demonstrated by numerical simulations.     

Passivity analysis of memristor-based recurrent neural networks with time-varying delays

This paper investigates the delay-dependent exponential passivity problem of the memristor-based recurrent neural networks (RNNs). Based on the knowledge of memristor and recurrent neural network, the model of the memristor-based RNNs is established. Taking into account of the information of the neuron activation functions and the involved time-varying delays, several improved results with less computational burden and conservatism have been obtained in the sense of Filippov solutions. A numerical example is presented to show the effectiveness of the obtained results.     

Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations

This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result.     

Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays

In this paper, some sufficient conditions are obtained for existence and global exponential stability of a unique equilibrium point of competitive neural networks with different time scales and multiple delays by using nonlinear Lipschitz measure (NLM) method and constructing suitable Lyapunov functional. The results of this paper are new and they complete previously known results.     

Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function

Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.     

Finite-time dynamic coverage for mobile sensor networks in unknown environments using neural networks

This paper addresses the finite-time dynamic coverage problem for mobile sensor networks in unknown environments. By introducing a condition where dynamic coverage of all points within the sensing range of each sensor exceeds the desired coverage level by a positive constant, a switching control strategy is developed to guarantee the achievement of desired coverage of the whole mission domain in finite time. The environment is modeled by a density function and neural networks are introduced to learn the function. Due to the approximation capability of neural networks, the proposed control scheme can learn the environment without a priori knowledge on the structure of the density function.     

Stability analysis of stochastic fuzzy Markovian jumping neural networks with leakage delay under impulsive perturbations

This paper investigates the global asymptotic stability of stochastic fuzzy Markovian jumping neural networks with mixed delays under impulsive perturbations in mean square. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delay and continuously distributed delay. By using the Lyapunov functional method, reciprocal convex approach, linear convex combination technique, Jensen integral inequality and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.     

Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses

In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results.     

Stabilization effect of diffusion in delayed neural networks systems with Dirichlet boundary conditions

In this paper, reaction–diffusion neural networks with unbounded time-varying delays and Dirichlet boundary conditions is studied. A new concept of global μ-stability in the sense of L² norm is introduced, and sufficient conditions are given to guarantee global μ-stability of the equilibrium point. The results obtained not only improve those in the earlier findings, but also show diffusion terms contribute to stabilization of neural networks systems.