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Highlights • The information-fusion-based state estimation problem for complex networks. • The complex networks are subject to time-delays and stochastic perturbations. • A fraction of network nodes is used for the addressed state estimation problem. • A neat mathematical analysis approach is developed to reflect the partial nodes. • The exponentially ultimately bounded state estimator is designed. Abstract This paper is concerned with the information-fusion-based state estimation problem for a class of discrete-time complex networks with time-varying delays and stochastic perturbations. The measurement outputs available for state estimation are from a fraction of network nodes, and the addressed problem is therefore referred to as the so-called Partial-Nodes-Based (PNB) state estimation problem. By employing the Lyapunov stability theory, a novel framework is established to cope with the PNB state estimation problem by the measurement outputs collected from partial network nodes. By constructing specific Lyapunov-Krasovskii functionals, sufficient criteria are derived for the existence of the desired exponentially ultimately bounded state estimator in mean square for the complex networks. Moreover, a special case is considered where the complex network under investigation is free of stochastic perturbations and the corresponding analysis issue is discussed to ensure the existence of an exponential state estimator. In addition, the explicit expressions of the gains of the desired estimators are characterized. Finally, a numerical illustrative example is presented to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the robust state estimation problem is investigated for a general class of uncertain discrete-time stochastic neural networks with probabilistic measurement delays. The measurement delays of the neural networks are described by a binary switching sequence satisfying a conditional probability distribution. The neural network under study involves parameter uncertainties, stochastic disturbances and time-varying delays, and the activation functions are characterized by sector-like nonlinearities. The problem addressed is the design of a full-order state estimator, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the estimation error is constrained to be robustly exponentially stable in the mean square and, at the same time, a prescribed disturbance rejection attenuation level is guaranteed. By using the Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are first established to ensure the existence of the desired estimators. These conditions are dependent on the lower and upper bounds of the time-varying delays. Then, the explicit expression of the desired estimator gains is described in terms of the solution to a linear matrix inequality (LMI). Finally, a numerical example is exploited to show the usefulness of the results derived. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov–Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions. [Copyright &y& Elsevier]

Abstract: This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov–Krasovskii functional, using the well-known S-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition. [Copyright &y& Elsevier]

Abstract This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

This paper discusses the distributed optimization problem for the continuous-time and discrete-time multi-agent systems. For such a problem, each agent possesses a local convex cost function only known by itself and all the agents converge to the optimizer of the sum of the local cost function through estimating the optimal states of the local cost function and exchanging states information between agents. Sufficient conditions for convergence to the optimizer of the continuous-time and discrete-time algorithms are provided by making use of the Lyapunov method. We also obtain the least convergence rate for the modified algorithm. Moreover, numerical simulations are supplied to testify the results we present. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sampled-data consensus problem for a class of nonlinear multiagent systems subject to cyber attacks. The considered attacks are assumed to be recoverable, which destroy the connectivity of the network topology with directed spanning tree. In light of the designed sampled-data control protocol, a more general switched system is proposed to model both the cyber attacks and the sampled-data mechanism within a unified framework. Then, by using the contradiction methods, the solution of a class of differential equations is provided to deal with the technical challenge resulting from the switching and sampling issues. Furthermore, in terms of such a solution combined with the constructed piecewise Lyapunov function, sufficient conditions are derived under which the nonlinear multiagent systems subject to attacks achieve the consensus exponentially. The relationship between the attack frequency and the sampling period is also revealed through the obtained conditions. Finally, simulations are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In the paper, the quaternion-valued neural networks (QVNNs) with non-differentiable time-varying delays are considered. Firstly, by using the method of plural decomposition, we decompose the QVNNs into two complex-valued neural networks. Some sufficient criteria in linear matrix inequality (LMI) form are derived to guarantee the existence and uniqueness of the equilibrium point for considered QVNNs by using the homeomorphism mapping principle of complex domain. Secondly, based on applying the free weighting matrix method and constructing appropriate Lyapunov–Krasovskii functional, several conditions are established in LMIs to ensure the the global μ − stability of QVNNs. Finally, by employing the predictor-corrector approach, two numerical examples are provided to show the feasibility and availability of the obtained result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative. [ABSTRACT FROM AUTHOR]

In this paper, the robust output feedback H ∞ control problem is investigated for a class of uncertain Takagi–Sugeno (T–S) fuzzy systems with missing measurements. In the underlying systems, both system parameters and missing probabilities are assumed to be effected by norm-bounded uncertainties which may reflect the reality more closely. The main purpose of this paper is to design a robust output feedback fuzzy controller such that the closed-loop system is asymptotically mean-square stable, and the disturbance rejection attenuation is constrained to a given level by means of the H ∞ performance index. Sufficient conditions are established via intensive analysis for the existence of the output feedback fuzzy controller, and the corresponding solvability conditions for the desired controller gains are derived. An illustrative example is provided to show the effectiveness of the developed design method. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive effects on the stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays are investigated. Several sufficient conditions are obtained ensuring the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks by the idea of vector Lyapunov function method, M-matrix theory and analytic technique. Moreover, the estimation for exponential convergence rate index is proposed. An example with simulations is provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the global uniform exponential stability problem of linear time‐varying systems with delayed impulsive effects. Two cases are considered: in the first case, the impulse‐free system is uniformly asymptotically stable and in the second case, the impulse‐free system may not be uniformly asymptotically stable. When the impulse‐free system is uniformly asymptotically stable, by the virtue of a uniformly asymptotically stable function, Lyapunov‐based sufficient conditions are derived to ensure the uniform exponential stability of linear time‐varying systems, where destabilizing and stabilizing impulses are considered, respectively. Different from existing results, the Lyapunov function is not assumed to decrease all the time and it is shown that under some conditions, the delayed impulsive effects are stabilizing. For the case that the impulse‐free system is not uniformly asymptotically stable, a time‐varying function is used to characterize the upper bound on the derivative of the Lyapunov function, and it is illustrated that the linear time‐varying systems can be stabilized by the delayed impulsive effects. Moreover, it is also shown that the impulsive input delay‐dependent criteria are less conservative than the delay‐independent ones when the impulsive input delay is small. Some examples are presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of robust output feedback control for a class of uncertain discrete-time delayed nonlinear stochastic systems with missing measurements. The parameter uncertainties enter into all the system matrices, the time-varying delay is unknown with given low and upper bounds, the nonlinearities satisfy the sector conditions, and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed performance level. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are first derived to guarantee the existence of the desired controllers, and then the controller parameters are characterized in terms of linear matrix inequalities (LMIs). A numerical example is exploited to show the usefulness of the results obtained. [Copyright &y& Elsevier]

In this paper, the periodicity of a class of impulsive Cohen–Grossberg-type fuzzy neural networks with hybrid delays is investigated. By applying integro-differential inequality with delays, the Lyapunov function, the Poincare map and the fixed point theory, we obtained some new sufficient conditions which guarantees the existence of periodic solutions and global exponential stability of the formulated system. Three numerical examples are given to show the effectiveness and generality of our method. [ABSTRACT FROM AUTHOR]

Abstract The periodicity problem of a class of Cohen–Grossberg-type fuzzy neural networks with impulses and time-varying delays is concerned in this paper. Via constructing a delay differential inequality, and applying fuzzy theory and the Lyapunov method, several criteria which ensure the existence and exponential stability of the periodic solutions for the considered systems are derived. An example is shown to illustrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper aims at the problem on state estimation of complex-valued neural networks with two additive time-varying delays. Via selecting appropriate Lyapunov–Krasovskii functionals and utilizing reciprocally convex approach and applying matrix inequality technique to analysis, a delay-dependent sufficient condition is derived in the form of linear matrix inequalities (LMIs) to estimate the neuron state with some observed output measurements so as to guarantee the global asymptotic stability of the error-state system. A numerical example is provided to illustrate the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the l 2 − l ∞ state estimation problem for discrete-time switched neural networks with time-varying delay. The main objective is to design a mode-dependent state estimator such that the error dynamics is exponentially stable with a weighted l 2 − l ∞ performance level. By incorporating the novel l 2 − l ∞ performance analysis approach, the augmented piecewise Lyapunov-like functionals, the discrete Wirtinger-based inequality and the average-dwell-time switching, less conservative sufficient conditions are proposed by means of linear matrix inequalities. A numerical example is given to illustrate the effectiveness and benefits of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the design and analysis problem of H ∞ filter for a class of nonlinear systems based on T-S fuzzy models with both multiplicative noises and redundant channels, which are governed by a set of Bernoulli distributed white sequences. The packet dropout’s probability of the i -th channel depends on random Bernoulli variables. The aim of this study is to design and analyze an H ∞ filter that can stabilize the T-S fuzzy filtering error dynamics. By utilizing both Lyapunov functional approach and stochastic analysis technique, we establish some sufficient conditions such that the addressed system is asymptotically stable in the mean square with a given H ∞ performance. The needed filtering parameters are obtained by making use of the matrix inequalities’ solution. In the end, an example is given to demonstrate the effectiveness and usefulness of the proposed filtering approach. [ABSTRACT FROM AUTHOR]

This paper discusses the stability in Lagrange sense for complex-valued neural networks with time-varying discrete delays and distributed delays as well as leakage delay. By constructing an appropriate Lyapunov–Krasovskii functional, and employing free-weighting-matrix approach and inequality techniques in matrix form, a sufficient criterion to guarantee global exponential stability in Lagrange sense is obtained for the investigated neural networks. The given criterion is delay-dependent and is shown as linear matrix inequalities in complex domain, which can be calculated numerically applying valid YALMIP toolbox in MATLAB. A numerical example is provided to manifest the validity of the proposed result. [ABSTRACT FROM AUTHOR]

The attention of this paper is mainly concentrated on the H ∞ state estimator's design problem for a kind of discrete-time memristive neural networks (MNNs) with multiple fading measurements. The phenomenon of multiple fading measurements is represented by a set of individual stochastic variables obeying a predetermined distribution on interval [0,1]. Firstly, the augmented system comprised of MNNs and the dynamics of estimation errors are put forward to implement the performance analysis. Then, under the framework of the difference inclusion theory combined with the Lyapunov function method, several sufficient conditions are established to guarantee the exponential mean-square stability as well as H ∞ performance index. Furthermore, the desired estimator parameter is obtained in view of the solution of a convex optimization problem. In the end, an illustrative numerical example is exploited to check the reliability and usefulness of the design scheme in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a new design problem of the H ∞ state estimator is developed for a kind of artificial neural networks (ANNs), where both infinite distributed delays and redundant channels are happening. These adopted redundant channels can effectively improve the reliability of networked systems from the viewpoint of engineering. Two series of stochastic variables satisfying Bernoulli distribution, are introduced to govern the infinite distributed delays and schedule the redundant channels. By utilizing both stochastic analysis and Lyapunov functional approach, we obtain a lot of sufficient conditions to ensure the desired H ∞ performance, while the mean-square stability is also satisfied for this investigated state estimation issues of ANNs. The needed estimator gains are designed making use of the matrix inequalities’ solution. In final, a simulation is showed to demonstrate the effectiveness and usefulness of the developed state estimator in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results. [ABSTRACT FROM AUTHOR]

In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations. [ABSTRACT FROM AUTHOR]