Stability and dissipativity analysis of static neural networks with time delay

Input-to-State Stability for Time-Delay Systems With Large Delays

In this article, we consider the input-to-state stability (ISS) problem for a class of time-delay systems with intermittent large delays, which may cause the invalidation of traditional delay-dependent stability criteria. The topic of this article features that it proposes a novel kind of stability criterion for time-delay systems, which is delay dependent if the time delay is smaller than a prescribed allowable size. While if the time delay is larger than the allowable size, the ISS can be preserved as well provided that the large-delay periods satisfy the kind of duration condition. Different from existing results on similar topics, we present the main result based on a unified Lyapunov-Krasovskii function (LKF). In this way, the frequency restriction can be removed and the analysis complexity can be simplified. A numerical example is provided to verify the proposed results.

Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach

This work investigates the stability and dissipativity problems for neural networks with time-varying delay. By the construction of new augmented Lyapunov-Krasovskii functionals based on integral inequality and the use of zero equality approach, three improved results are proposed in the forms of linear matrix inequalities. And, based on the stability results, the dissipativity analysis for NNs with time-varying delays was investigated. Through some numerical examples, the superiority and effectiveness of the proposed results are shown by comparing the existing works.

Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point Measurements

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

Dissipativity Analysis for Neural Networks With Time-Varying Delays via a Delay-Product-Type Lyapunov Functional Approach

This article is concerned with the problem of dissipativity and stability analysis for a class of neural networks (NNs) with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional (LKF), including some delay-product-type terms, is proposed, in which the information on time-varying delay and system states is taken into full consideration. Second, by employing a generalized free-matrix-based inequality and its simplified version to estimate the derivative of the proposed LKF, some improved delay-dependent conditions are derived to ensure that the considered NNs are strictly ( Q , S , R )- γ -dissipative. Furthermore, the obtained results are applied to passivity and stability analysis of delayed NNs. Finally, two numerical examples and a real-world problem in the quadruple tank process are carried out to illustrate the effectiveness of the proposed method.

Relaxed Stability Criteria for Neural Networks With Time-Varying Delay Using Extended Secondary Delay Partitioning and Equivalent Reciprocal Convex Combination Techniques

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.

A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks

In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model.

Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties

We study the robust dissipativity issue with respect to the Hopfield-type of complex-valued neural network (HTCVNN) models incorporated with time-varying delays and linear fractional uncertainties. To avoid the computational issues in the complex domain, we divide the original complex-valued system into two real-valued systems. We devise an appropriate Lyapunov-Krasovskii functional (LKF) equipped with general integral terms to facilitate the analysis. By exploiting the multiple integral inequality method, the sufficient conditions for the dissipativity of HTCVNN models are obtained via the linear matrix inequalities (LMIs). The MATLAB software package is used to solve the LMIs effectively. We devise a number of numerical models and their empirical results positively ascertain the obtained results.

Stability Analysis for Delayed Neural Networks With an Improved General Free-Matrix-Based Integral Inequality

This paper revisits the problem of stability analysis for neural networks with a time-varying delay. An improved general free-matrix-based (FMB) integral inequality is proposed with an undetermined number m . Compared with the conventional FMB ones, the improved inequality involves a much smaller number of free matrix variables. In particular, the improved FMB integral inequality is expressed in a concrete form for any value of m . By employing the new inequality with a properly constructed Lyapunov-Krasovskii functional, a new stability condition is derived for neural networks with a time-varying delay. Two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens.

Stability Analysis for Neural Networks With Time-Varying Delay via Improved Techniques

This paper is concerned with the stability problem for neural networks with a time-varying delay. First, an improved generalized free-weighting-matrix integral inequality is proposed, which encompasses the conventional one as a special case. Second, an improved Lyapunov-Krasovskii functional is constructed that contains two complement triple-integral functionals. Third, based on the improved techniques, a new stability condition is derived for neural networks with a time-varying delay. Finally, two widely used numerical examples are given to demonstrate that the proposed stability condition is very competitive in both conservatism and complexity.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Extended dissipative filter design for T-S fuzzy systems with multiple time delays

This paper deals with the fuzzy filtering problem for a class of nonlinear time-delay systems described by T-S fuzzy models. Different from the existing schemes in the literature, this paper aims to solve the fuzzy filtering problem by considering the H_∞, L₂ - L_∞ and dissipative performance constraints in a unified way. To achieve this purpose, the recently proposed notion of extended dissipativity is applied, which provides an inequality covering the well-known H_∞, L₂ - L_∞ and dissipative performances. Another purpose of this paper is to design filters involving communication delays. Such filters have a more general form than the delay-free filters that have been largely considered in the traditional studies. In order to design the fuzzy filters under consideration, a novel fuzzy Lyapunov-Krasovskii functional is employed, and delay-dependent conditions for stability and performance analysis of the filtering error system are obtained. Then, LMI-based conditions for the existence of the desired filters are presented. The filter parameters can be obtained by solving the presented LMIs. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.

New Conditions for Global Asymptotic Stability of Memristor Neural Networks

Recent papers in the literature introduced a class of neural networks (NNs) with memristors, named dynamic-memristor (DM) NNs, such that the analog processing takes place in the charge-flux domain, instead of the typical current-voltage domain as it happens for Hopfield NNs and standard cellular NNs. One key advantage is that, when a steady state is reached, all currents, voltages, and power of a DM-NN drop off, whereas the memristors act as nonvolatile memories that store the processing result. Previous work in the literature addressed multistability of DM-NNs, i.e., convergence of solutions in the presence of multiple asymptotically stable equilibrium points (EPs). The goal of this paper is to study a basically different dynamical property of DM-NNs, namely, to thoroughly investigate the fundamental issue of global asymptotic stability (GAS) of the unique EP of a DM-NN in the general case of nonsymmetric neuron interconnections. A basic result on GAS of DM-NNs is established using Lyapunov method and the concept of Lyapunov diagonally stable matrices. On this basis, some relevant classes of nonsymmetric DM-NNs enjoying the property of GAS are highlighted.

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

An Improved Result on Dissipativity and Passivity Analysis of Markovian Jump Stochastic Neural Networks With Two Delay Components

In this paper, we investigate the dissipativity and passivity of Markovian jump stochastic neural networks involving two additive time-varying delays. Using a Lyapunov-Krasovskii functional with triple and quadruple integral terms, we obtain delay-dependent passivity and dissipativity criteria for the system. Using a generalized Finsler lemma (GFL), a set of slack variables with special structure are introduced to reduce design conservatism. The dissipativity and passivity criteria depend on the upper bounds of the discrete time-varying delay and its derivative are given in terms of linear matrix inequalities, which can be efficiently solved through the standard numerical software. Finally, our illustrative examples show that the proposed method performs well and is successful in problems where existing methods fail.

Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays

This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.

Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov-Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.