Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design.

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall-Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov-Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.

A general framework for robust stability analysis of neural networks with discrete time delays.

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper.

Asynchronous dissipative stabilization for stochastic Markov-switching neural networks with completely- and incompletely-known transition rates.

The asynchronous dissipative stabilization for stochastic Markov-switching neural networks (SMSNNs) is investigated. The aim is to design an output-feedback controller with inconsistent mode switching to ensure that the SMSNN is stochastically stable with extended dissipativity. Two situations, which involve completely- and incompletely-known transition rates (TRs), are taken into account. The situation that all TRs are exactly known is considered first. By applying a mode-dependent Lyapunov-Krasovskii functional, Dynkin's formula, and several matrix inequalities, a criterion for the desired performance of the closed-loop SMSNN is derived and a design method for determining the asynchronous controller is developed. Then, the study is generalized to the situation where some TRs are allowed to be uncertain or even fully unknown. An inequality is established for judging the upper bound of the product of the TRs with the Lyapunov matrix by making full use of accessible information on the incompletely-known TRs. Based on the inequality, performance analysis and control synthesis are presented without imposing the zero-sum hypothesis of the uncertainties in the TR matrix. Finally, an example with numerical calculation and simulation is provided to verify the validity of the stabilizing approaches.

A novel Lyapunov stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays.

The major target of this research article is to conduct a new Lyapunov stability analysis of a special model of Cohen-Grossberg neural networks that include multiple delay terms in state variables of systems neurons and multiple delay terms in time derivatives of state variables of systems neurons in the network structure. Employing some proper linear combinations of three different positive definite and positive semi-definite Lyapunov functionals, we obtain some novel sufficient criteria that guarantee global asymptotic stability of this type of multiple delayed Cohen-Grossberg type neural systems. These newly derived stability results are determined to be completely independent of the involved time delay terms and neutral delay terms, and they are totally characterized by the values of the interconnection parameters of Cohen-Grossberg neural system. Besides, the validation of the obtained stability criteria can be justified by applying some simple appropriate algebraic equations that form some particular relations among the constant system elements of the considered neutral neural systems. A useful and instructive numerical example is analysed to exhibit some major advantages and novelties of these newly proposed global stability results in this paper over some previously reported corresponding asymptotic stability conditions.

Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal.

This study deals with the finite-time synchronization problem of a class of switched complex dynamical networks (CDNs) with distributed coupling delays via sampled-data control. First, the dynamical model is studied with coupling delays in more detail. The sampling system is then converted to a continuous time-delay system using an input delay technique. We obtain some unique and less conservative criteria on exponential stability using the Lyapunov-Krasovskii functional (LKF), which is generated with a Kronecker product, linear matrix inequalities (LMIs), and integral inequality. Furthermore, some sufficient criteria are derived by an average dwell-time method and determine the finite-time boundedness of CDNs with switching signal. The proposed sufficient conditions can be represented in the form of LMIs. Finally, numerical examples are given to show that the suggested strategy is feasible.

Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks with uncertain parameters and time-varying delays.

In this paper we investigate controller design problem for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks (FMCVBAMNNs) with uncertain parameters and time-varying delays. By using the Lyapunov theory, differential inclusion theory, and fractional calculus theory, finite-time stabilization condition for fractional-order memristive complex-valued BAM neural networks and the upper bound of the settling time for stabilization are obtained. The nonlinear complex-valued activation functions are split into two (real and imaginary) components. Moreover, the settling time of fixed time stabilization, that does not depend upon the initial values, is merely calculated. A novel criterion for guaranteeing the fixed-time stabilization of FMCVBAMNNs is derived. Our control scheme achieves system stabilization within bounded time and has an advantage in convergence rate. Numerical simulations are furnished to demonstrate the effectiveness of the theoretical analysis.

Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters.

This paper deals with the anti-synchronization issue for stochastic delayed reaction-diffusion neural networks subject to semi-Markov jump parameters. A resilient fault-tolerant controller is utilized to ensure the anti-synchronization in the presence of actuator failures as well as gain perturbations, simultaneously. Firstly, by means of the Lyapunov functional and stochastic analysis methods, a mean-square exponential stability criterion is derived for the resulting error system. It is shown the obtained criterion improves a previously reported result. Then, based on the present analysis result and using several decoupling techniques, a strategy for designing the desired resilient fault-tolerant controller is proposed. At last, two numerical examples are given to illustrate the superiority of the present stability analysis method and the applicability of the proposed resilient fault-tolerant anti-synchronization control strategy, respectively.

New Criteria for Stability of Neutral-Type Neural Networks With Multiple Time Delays.

This research work studies stability problems for more general models of neutral-type neural systems where both neuron states and the time derivative of neuron states involve multiple delays. Some new sufficient criterion is presented, which guarantee the existence, uniqueness, and global asymptotic stability of equilibrium points of the considered neural network model. These obtained stability conditions, which can be applied to some larger classes of general neural network models, are based on the analysis of a new and improved suitable Lyapunov functional. The proposed conditions are independent of time delay parameters and can be easily justified by examining some certain relationships among the relevant neural network parameters. This paper also shows that the obtained stability criteria can be considered as the generalization of some previously reported corresponding stability conditions for neural networks, including multiple time delay parameters.

Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control.

This paper investigates state estimation for complex dynamical networks (CDNs) with time-varying delays by using sampled-data control. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling state estimator is transformed into a continuous time-delay system with stochastic parameters in the system matrices, where the purpose is to design a state estimator to estimate the network states through available output measurements. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) containing triple and fourth integral terms and applying Wirtinger-based single and double integral inequality, Jenson integral inequality technique, delay-dependent stability conditions are established. The obtained conditions can be readily solved by using the LMI tool box in MATLAB. Finally, a numerical example is provided to demonstrate the validity of the proposed scheme.

Event-triggered H∞ filtering for delayed neural networks via sampled-data.

This paper is concerned with event-triggered H∞ filtering for delayed neural networks via sampled data. A novel event-triggered scheme is proposed, which can lead to a significant reduction of the information communication burden in the network; the feature of this scheme is that whether or not the sampled data should be transmitted is determined by the current sampled data and the error between the current sampled data and the latest transmitted data. By constructing a proper Lyapunov-Krasovskii functional, utilizing the reciprocally convex combination technique and Jensen's inequality sufficient conditions are derived to ensure that the resultant filtering error system is asymptotically stable. Based on the derived H∞ performance analysis results, the H∞ filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, the proposed stability conditions are demonstrated with numerical example.

Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays.

In this study, we present an approach for the decentralized event-triggered synchronization of Markovian jumping neutral-type neural networks with mixed delays. We present a method for designing decentralized event-triggered synchronization, which only utilizes locally available information, in order to determine the time instants for transmission from sensors to a central controller. By applying a novel Lyapunov-Krasovskii functional, as well as using the reciprocal convex combination method and some inequality techniques such as Jensen's inequality, we obtain several sufficient conditions in terms of a set of linear matrix inequalities (LMIs) under which the delayed neural networks are stochastically stable in terms of the error systems. Finally, we conclude that the drive systems synchronize stochastically with the response systems. We show that the proposed stability criteria can be verified easily using the numerically efficient Matlab LMI toolbox. The effectiveness and feasibility of the results obtained are verified by numerical examples.

An improved robust stability result for uncertain neural networks with multiple time delays.

This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.

A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks.

The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.

Robust stability analysis of a class of neural networks with discrete time delays.

This paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.

Global robust stability of bidirectional associative memory neural networks with multiple time delays.

This correspondence presents a sufficient condition for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point for bidirectional associative memory neural networks with discrete time delays. The results impose constraint conditions on the network parameters of the neural system independently of the delay parameter, and they are applicable to all bounded continuous nonmonotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.

Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays.

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

An analysis of exponential stability of delayed neural networks with time varying delays.

This paper derives a new sufficient condition for the exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a Lyapunov-Krasovskii functional and using Linear Matrix Inequality (LMI) approach. This result establishes a relation between the delay time and the parameters of the network. The result is also compared with the most recent result derived in the literature.