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This article focuses on investigating the synchronization and position/force tracking performance of the multilateral teleoperation system with asymmetric time delays. First, the synchronization and tracking error signals are proposed to transform the nonlinear dynamic system into a closed-loop system governed by the Markovian jumping parameter. Because of the presence of time delays, the information regarding the system states might become unavailable. Owing to this, a feedback control based on the hidden Markov model is developed through which the information on the current state of the actual system can be accessed through a series of observations. Moreover, the forward and backward delays of the master and slave manipulators are assumed to be asymmetric and varying with time. For the stability analysis, the Lyapunov–Krasovskii technique has been adopted for which its derivatives are dealt by employing Jensens’ inequality and extended reciprocal convex matrix inequality. Finally, simulation results were provided to validate the proposed methodology guaranteeing the closed-loop system to be asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, we study a projective multi-synchronization problem for fractional-order complex-valued coupled multi-stable neural networks (FCVCMNNs) with time-delays. Using a complex decomposition approach, FCVCMNNs are divided into their real and imaginary components. Our method uses certain conditions for each subnetwork to achieve the multiple local equilibrium points or stable periodic orbits that are exponentially stable, which, when combined with the Lyapunov functions method, result in FCVCMNNs that are projectively multi-synchronized. The FCVCMNNs, on the other hand, are examined directly through the use of the Lyapunov functional method and linear matrix inequality (LMI). Various new sufficient conditions in the form of complex-valued LMIs are presented for the projective multi-synchronization of the considered FCVCMNNs. As a final step, we provide two numerical simulations to verify the effectiveness of the main results derived in this paper. [ABSTRACT FROM AUTHOR]

The stabilization of fault-tolerant control problem for the doubly fed induction generator (DFIG)-based wind turbine (WT) model has been investigated with stochastic actuator faults by incorporating a Takagi–Sugeno (T–S) fuzzy technique. To depict such stochastic actuator faults, the proposed model is incorporated with Markovian switching parameters for denoting various faulty modes. Besides, a novel fault-tolerant fuzzy switching control with sampled-data (SD) inputs has also been employed for eliminating the stochastic faults so that the stabilization of the system and an optimal ${\mathsf {H}}_{\infty }$ level could be ensured simultaneously. Furthermore, the stability conditions are derived by employing fuzzy Lyapunov–Krasovskii functionals (LKFs), whose matrices are membership dependent functions. Finally, the proposed control method for the stabilization problem is validated through a numerical simulation performed on the DFIG-based WT model. [ABSTRACT FROM AUTHOR]

Abstract This paper is mainly concerned with an investigation of antigen-driven T-cell infection process through a mathematical model. Several mathematical models have been introduced in the literature in order to gain insights into the dynamics of the disease progression, however, the results considering the effect of multiple factors which include antigen-driven CD4 T-cell progress, latent infection stage, activation of CTLs response, role of antiretroviral therapies (ARTs) and possibilities of multiple time-delays during the infection process are not involved. Hence, the paper introduces a six-dimensional virus infection model by involving the above factors. Particularly, (i) the effect of activation of antigen-specific T-cells; (ii) the effect of the maturation of infected cells; (iii) effect of multiple time delays, that is, during the interaction between susceptible and infectious and during the activation of immune responses; which play a significant role in preventing and modulating the Human Immunodeficiency Virus (HIV). The main aim of the paper to analyze the local and global stability of the class of mathematical models regarding the effect of time delays which provides a better pathway to the infection progress. Finally, the overall contribution of the present work is listed as follows: (1) by constructing the suitable Lyapunov functional, the global stability of the intracellular delayed model is derived; (2) detailed Hopf-bifurcation analysis is discussed with respect to immune response delay. The numerical simulation is performed to validate the effectiveness and applicability of the theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper investigates H ∞ state estimation problem for a class of semi-Markovian jumping discrete-time neural networks model with event-triggered scheme and quantization. First, a new event-triggered communication scheme is introduced to determine whether or not the current sampled sensor data should be broad-casted and transmitted to the quantizer, which can save the limited communication resource. Second, a novel communication framework is employed by the logarithmic quantizer that quantifies and reduces the data transmission rate in the network, which apparently improves the communication efficiency of networks. Third, a stabilization criterion is derived based on the sufficient condition which guarantees a prescribed H ∞ performance level in the estimation error system in terms of the linear matrix inequalities. Finally, numerical simulations are given to illustrate the correctness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper mainly deals with the problem of designing delayed state-feedback controller for neural networks with leakage delay. By constructing an appropriate Lyapunov–Krasovskii functional including double integral terms having two different exponential decay rates and utilizing linear matrix inequality (LMI) technique with the help of slack variables, some sufficient conditions for globally exponential stabilization results are obtained by designing of delayed state-feedback controller. The novelty of this paper includes: (i) although many papers dealt with dynamics of neural networks with leakage delay, there is little work on design of feedback controller. Even there is almost no result that deals with the delay-feedback controller for such delay systems, which is the main motivation of this paper; (ii) the derived delay-dependent stability criteria establish the relationship between leakage delay and time delay in the feedback term, which can be easily checked via the MATLAB LMI toolbox; (iii) we consider the general case that the control term is given in the form of B u , where B is an n × m real matrix. Such case is more difficult to handle than the special case that B is unit matrix. It indicates that the controller can be used in all states or in some states by proper selection of the matrix B . The effectiveness of the proposed method in this paper is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]

The main intention of this study is to develop a sampled-data H∞ fuzzy controller design to analyze the stability of coupled ordinary differential equation (ODE)-partial differential equation (PDE) systems, where the nonlinear coupled system is expressed by Takagi-Sugeno (T-S) fuzzy models. The coupled ODE-PDE system in this paper constitutes an n-dimensional nonlinear subsystem of ODEs and a scalar linear parabolic subsystem of PDE. Then, in regard to the T-S model representation, Lyapunov technique is utilized to model a sampled-data H∞ fuzzy controller to stabilize the contemplated coupled systems and to attain a desired H∞ disturbance attenuation performance. The formulated time-dependent Lyapunov functional makes full use of the accessible information about the actual sampling pattern. The outcome of the sampled-data H∞ fuzzy control problem is expressed as linear matrix inequality (LMI) optimization problem which can be solved effectively by using any of the available softwares. Finally, hypersonic rocket car model is furnished with simulation results to exhibit the efficacy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of stability and synchronization of fractional-order complex-valued neural networks with time delay. By using Lyapunov-Krasovskii functional approach, some linear matrix inequality (LMI) conditions are proposed to ensure that the equilibrium point of the addressed neural networks is globally Mittag-Leffler stable. Moreover, some sufficient conditions for projective synchronization of considered fractional-order complex-valued neural networks are derived in terms of LMIs. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper the problem of extended dissipative state estimation for discrete-time switched complex dynamical networks (CDNs) with mixed time delays is investigated. The switching approach is based on sojourn probabilities and it is assumed that these probabilities are known aprior. One primary channel and multiredundant channels which constitute multiple communication channels are considered to coexist for the state estimation of underlying switched CDNs. To solve for the H ∞ , l 2 − l ∞ , passive and dissipative state estimation, the concept of the extended dissipativity is used by adjusting the weighting matrices in a new performance index. Suitable Lyapunov–Krasovskii functional is constructed in terms of Kronecker product and based on the Lyapunov stability theory, new delay-dependent sufficient stability conditions are derived in terms of linear matrix inequalities (LMIs). The effectiveness of the developed theoretical results is demonstrated via a numerical example. [ABSTRACT FROM AUTHOR]

On the basis of the passivity theory, the problem of designing non-fragile [ABSTRACT FROM AUTHOR]

This paper concerns the problem ofstate estimation of discrete-time Markov jump neural networks with general transition probabilities and output quantization. In terms of a Markov chain, the event of mode switching at various times is considered in both the parameters and the discrete delays of the neural networks. The state estimation is analyzed when the information is transmitted over a digital communication channel. In this concern the design of the quantizer and the estimator is jointly investigated. The purpose of the concerned problem is to design a mode-dependent state estimator such that the network states are estimated through available output measurements such that the dynamics of the estimation error is stochastically stable. Novel Lyapunov–Krasovskii functional is constructed and sufficient constraints are derived in terms of linear matrix inequalities such that the existence of the desired estimator is assured. The effectiveness of the proposed approach is illustrated through a simulation example. [ABSTRACT FROM PUBLISHER]

In this study, the state estimation and H ∞ control problem for discrete-time switched neural networks with mode-dependent time-varying delays has been studied with persistent dwell time (PDT) switching regularities. The phenomenon of PDT, existing for the designed estimator of underlying switched neural networks are characterized by introducing a Bernoulli distributed white sequence. The main aim of the addressed problem is to design mode dependent state estimators such that the dynamics of the estimation error is exponentially stable with an expected decay rate and satisfies the prescribed H ∞ performance constraint. Sufficient conditions are established for the occurence of the desired filter to ensure the mean-square exponential stability of the augmented system by using the generalized Finsler’s lemma and then the full-order filter parameters are presented in terms of solutions to a set of linear matrix inequality (LMI) conditions. Finally, simulation results are given to explain the usefulness of the proposed design procedure. [ABSTRACT FROM AUTHOR]

This study is concerned with the synchronization problem of nonlinear singularly perturbed complex networks with time-varying coupling delays. In an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria. By developing the novel Lyapunov–Krasovskii functional, some adequate conditions which ensure the asymptotic synchronization are obtained in the form of linear matrix inequalities. Besides that, synchronization problem of nonlinear singularly perturbed complex networks with uncertain inner coupling are also taken into account. The uncertain inner coupling is represented by making use of the interval matrix approach. Finally, simulation results are displayed to show the efficacy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the exponential $$H_{\infty }$$ synchronization criteria for complex dynamical networks of Lur'e- type systems with non-delay and delay couplings as well as external disturbances. The pinning sampled-data control is designed to achieve synchronization, in which only the selection of nodes is controlled, instead of the whole network. By constructing an improved Lyapunov-Krasovskii functional and utilizing the reciprocal convex method, the sufficient conditions are expressed in terms of linear matrix inequalities to ensure synchronization of the proposed network with a guaranteed $$H_{\infty }$$ performance. Different from most existing studies, the addressed synchronization criteria depend not only on the upper bounds of the sampling intervals but also on the lower bounds; therefore, potentially leading to reduced conservative criteria. The desired control gain matrices are calculated by solving the obtained linear matrix inequalities that guarantee the exponential stability of the error system under the $$H_{\infty }$$ norm. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential synchronization of Lur’e type complex dynamical networks with uncertain coupling strength. A novel pinning impulsive controller is designed to achieve synchronization, in which, only selection of nodes are chosen to control instead of the whole network. In addition, the proposed control scheme is digital and it can lead to low installation cost and less time. In order to realize synchronization of Lur’e type complex dynamical networks, crucial delay-dependent stability conditions are derived by utilizing Lyapunov functional together with information of the time-varying delay and convex combination technique. The resulting stability conditions are formulated in the form of linear matrix inequalities (LMIs) and by solving the obtained LMIs, desired impulsive control gain matrices are calculated, which are capable to guarantee the exponential stability of error system. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delay for analyzing the dynamic behaviors such as local asymptotic stability and Hopf bifurcation. In the case of a neural network with hub and ring structure, the stability of the equilibrium state is investigated by analyzing the eigenvalue of the corresponding characteristic matrix for the hub and ring structured fractional-order time delay models using a Laplace transformation for the Caputo-fractional derivatives. Some sufficient conditions are established to guarantee the uniqueness of the equilibrium point. In addition, conditions for the occurrence of a Hopf bifurcation are also presented. Finally, numerical examples are given to demonstrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust exponential stabilization of offshore steel jacket platforms, where linear fractional uncertainties and randomly occurring uncertainties are taken into account. In this work, we introduce a sampled-data controller with m stochastically varying sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov-Krasovskii functional with triple integral terms based on the extended writinger's inequality is constructed and some sufficient conditions that guarantee the exponential stabilization of considered system are derived in terms of linear matrix inequalities by using Jensen's inequality and reciprocally convex technique. Finally, a numerical example is presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The intention of this paper is to explore the problem of pinning sampled-data synchronization of coupled reaction-diffusion neural networks with added inertia and time-varying delays. Through the proper variable substitution, the original system is transferred into first-order differential equations. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF), which uses more information of the delay bounds, global asymptotic synchronization criteria for the considered system are established in the form of LMIs. The acquired LMIs can be simply examined for their practicability by utilizing any of the accessible softwares. At last, two examples are furnished to manifest the efficacy of the derived criteria. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction-diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction-diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov-Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. [ABSTRACT FROM AUTHOR]

This paper presents the synchronization criteria for two identical delayed chaotic Lur'e systems. Here, we employ network reliable feedback control for achieving synchronization between our considered systems. The advantage of the employed controller lies in the fact that it even works in the case of actuator or sensor failures, which may occur in many real-world situations. By introducing an improved Lyapunov-Krasovskii (L-K) functional and by using reciprocally convex technique, sufficient conditions are given in the form of linear matrix inequalities (LMIs) to ensure asymptotic stability of resulting synchronization error system. Numerical simulations of neural networks and Chua's circuit system are given to verify the effectiveness and less conservatism of the presented theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the periodicity and synchronization of inertial memristive neural networks with supremums and time delays. The analysis in this paper employs the results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. Further, by employing the second order differential inclusion theory and then choosing suitable variable transformation, the original system can be transformed into first order differential equations. By using the matrix measure method and Halany inequality techniques, the sufficient condition that guarantee the global exponential synchronization of drive-response system of coupled inertial memristive neural networks via the state feedback controller is derived. Furthermore, the global exponential periodicity of the addressed neural networks is also discussed. Finally, numerical examples and simulations are given to demonstrate the validation of the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of μ -stability analysis of memristor-based recurrent neural networks with the effects of bounded and unbounded leakage time-varying delays. A new idea of μ -stability analysis of neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Two types of memductance functions is used to derive the proposed stability results. Obviously, the memristive neural network with different memductance functions is a state-dependent switched system or a state-dependent continuous system, which is the generalization of those for conventional artificial neural networks. Under the framework of Filippov solutions, μ -stability analysis of solutions for functional differential inclusions and memristor-based neural networks can be guaranteed by constructing suitable Lyapunov–Krasovskii functionals, suitable inequalities and LMIs. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. Leakage time-varying delay is considered in this paper to be bounded, unbounded and differentiable. Taking into account of the information of the neuron activation functions and unbounded time-varying delays, several improved results have been obtained in terms of LMIs and these are tested by MATLAB LMI toolbox. The model based on the memristor widens the relevance scope for the design of neural networks, and the new effective results also enrich the toolbox for the qualitative analysis of neural networks. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to bemin number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov–Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the global O ( t − α ) stability and global asymptotic periodicity for a class of fractional-order complex-valued neural networks (FCVNNs) with time varying delays is investigated. By constructing suitable Lyapunov functionals and a Leibniz rule for fractional differentiation, some new sufficient conditions are established to ensure that the addressed FCVNNs are globally O ( t − α ) stable. Moreover, some sufficient conditions for the global asymptotic periodicity of the addressed FCVNNs with time varying delays are derived, showing that all solutions converge to the same periodic function. Finally, numerical examples are given to demonstrate the effectiveness and usefulness of our theoretical results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of leakage-delay-dependent stability analysis of Markovian jumping linear systems with time-varying delays and nonlinear perturbations. Mixed time-varying delays, which include leakage, discrete, and distributed delays, pertaining to the proposed system are addressed. Based on an improved Lyapunov–Krasovskii functional with triple integral terms and by employing the model transformation technique and the reciprocal convex method, the sufficient conditions for the delay-dependent stability of the considered system are derived. Moreover, the sufficient conditions obtained are formulated in terms of linear matrix inequalities to achieve the global asymptotical stability in mean square of the considered delayed system. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Memristor is the new model two-terminal nonlinear circuit device in electronic circuit theory. This paper deals with the problem of global dissipativity and global exponential dissipativity for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays. Sufficient global dissipativity conditions are derived from the theory of M-matrix analysis, and the globally attractive set as well as the positive invariant set is established. By constructing Lyapunov-Krasovskii functionals and using a linear matrix inequality technique, some new sufficient conditions on global dissipativity and global exponential dissipativity of MCVNNs are derived. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, impulsive synchronization of stochastic memristor-based recurrent neural networks with time delay is studied. One can find that the memristive connection weights have a certain relationship with the stability of the system. Based on the drive-response concept, the stochastic differential inclusions theory and the Lyapunov functional method with the impulsive delay differential inequality technique was established to guarantee the impulsive synchronization of memristor-based recurrent neural networks with stochastic effects. The obtained sufficient conditions can be checked easily by Linear Matrix Inequalities (LMI) Control Toolbox in MATLAB. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of stability analysis of generalized neural networks with time delays. It should be noted that additive time-varying delays are taken in the state of the neural networks. A novel augmented Lyapunov–Krasovskii (L–K) functional which involves more information on the activation function of the neural networks and upper bound of the additive time-varying delays is constructed. By introducing some zero equations and using the reciprocal convex combination technique and Finsler׳s lemma, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall’s inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α : 1 < α < 2 and 0 < α < 1 . The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov–Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem is investigated for a networked multi-teleoperator system (NMTS) under a stochastic sampled-data controller. By utilizing the input delay approach, the sampling period is transformed into a time-varying yet bounded delay. With the help of algebraic graph theory and probability theory, a new consensus protocol is designed. Subsequently, a sufficient condition for the leader-following consensus of NMTS is derived in the form of linear matrix inequality (LMI) by constructing an appropriate Lyapunov–Krasovskii functional and by utilizing some matrix and integral inequality techniques. Based on the derived condition, the design method of the desired sampled-data controller is also obtained in terms of the solution to LMI which can be checked effectively by using available software. In addition, the effectiveness of the obtained theoretical results is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper addresses pinning sampled-data synchronization problem for complex dynamical networks with probabilistic time-varying coupling delays and control packet loss. The sampling period considered here is assumed to be less than a given bound. By introducing a Bernoulli distributed stochastic variable, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. A new Lyapunov–Krasovskii functional (LKF) is constructed and by using quadratic convex approach, reciprocal convex technique and Jensen׳s inequality, sufficient conditions for the synchronization of complex networks are derived. Based on the average dwell-time method and delay-probability-distribution-dependent condition, the synchronization criterion is derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

The objective of this paper is to inspect the leader-following consensus of distributed multi-agent system (MAS) under sampled-data control. The communication flow among neighbor agents is described by an undirected graph. The control protocols are designed by using sampling period technique and zero-order hold circuit along with missing data. A stochastic variable satisfying Bernoulli distributed white noise sequences is introduced to model the missing data. Moreover, by employing the input-delay approach, we transform the sampling data into time-varying delayed data and on the basis of receiving data, two sampled-data control models are proposed. Through the construction of a suitable Lyapunov–Krasovskii functional and by the utilization of integral inequalities, new delay-dependent consensus conditions for the concerned system are derived in the form of linear matrix inequalities (LMIs) which can be readily solved by utilizing any of the valid software packages. The effectiveness of the proposed algorithms is illustrated by two numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of stochastic sampled-data H∞ control for a class of parabolic systems governed by one-dimensional semilinear transport reaction systems with external disturbances. A sampled-data controller design is developed by introducing the time-varying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampled-data control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger's inequality. With this new approach, sufficient conditions that guarantee the asymptotic mean-square stabilization of the considered systems and the L2-gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of global μ -stability for complex-valued neural networks (CVNNs) with unbounded time-varying delays and it has been widely investigated. Under mild conditions, some new sufficient conditions for global μ -stability of considered CVNNs are derived. Moreover, some new sufficient conditions are obtained to ensure the global μ -stability of CVNNs in the form of complex-valued LMIs as well as real-valued LMIs by using an appropriate Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). Both of complex-valued LMIs as well as real-valued LMIs are easily solved by using standard numerical algorithms. Finally, two numerical examples are presented to demonstrate the effectiveness and usefulness of our theoretical results. [ABSTRACT FROM AUTHOR]

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen’s inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen’s inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The objective of this paper is to analyze the stability of switched Hopfield neural networks of neutral type with additive time-varying discrete delay components and finitely distributed delay. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Finsler׳s lemma, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities to ensure the asymptotic stability of the equilibrium point of the considered neural networks. The derived criteria use the information of the upper delay bounds, which may lead to conservativeness. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique. In order to achieve synchronization for identical chaotic systems, a memristor-based Lorenz system is considered as both master and slave systems, and for nonidentical chaotic systems, memristor-based Lorenz and Chuas systems are considered as master and slave systems, respectively. Based on the Lyapunov stability theory and active backstepping control technique, proper controllers are designed to achieve synchronization. Finally, numerical simulations are provided to show the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we are considered complex-valued neural networks (CVNNs) with unbounded time-varying delays and the problem of multiple μ-stability of the proposed CVNNs is extensively investigated. The choice of activation function is the main challenge in the analysis of CVNNs. Therefore, we chosen the real-imaginary-type activation function for the considered CVNNs. Some new sufficient conditions are derived to ensure that existence of [ ( 2 α + 1 ) ( 2 β + 1 ) ] n ( α , β ≥ 1 ) equilibrium points in which [ ( α + 1 ) ( β + 1 ) ] n equilibrium points are locally μ-stable and the remaining equilibrium points [ ( 2 α + 1 ) ( 2 β + 1 ) ] n − [ ( α + 1 ) ( β + 1 ) ] n are unstable for the considered CVNNs. Based on our main results, we can derive some stability conditions such as multiple exponential stability, multiple power stability, multiple log-stability and multiple log–log-stability. Finally, numerical example is presented to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay via a stochastic sampled-data controller. In addition, the sampling period is assumed to be time-varying and switches between $$m$$ different values in a random way with given probability. By constructing a new Lyapunov-Krasovskii functional (LKF) with triple integral terms and by employing convex combination technique and free weighting matrices method, sufficient conditions for the coupled complex dynamical network to be globally exponentially synchronized in the mean square sense are derived. The information about the lower bound of the discrete time-varying delay is used in the LKF. Based on the derived condition, the desired sampled-data feedback controller is designed in terms of the solution to linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, synchronization of two different fractional-order memristor-based chaotic systems is considered. To achieve synchronization, an active control technique is used. The main proof is concerned with the problem of synchronization of memristor-based Lorenz systems with memristor-based Chua's circuits. Numerical simulations of fractional-order memristor-based chaotic systems are performed by using the Caputo version and a predictor-corrector algorithm for fractional-order differential equations, which is a generalization of the Adams-Bashforth-Moulton method. From the simulations, it will be verified that the proposed control method is effective in achieving synchronization. [ABSTRACT FROM AUTHOR]

In this letter, the problem of stability analysis for neutral type Lur’e systems with interval time-varying delays is considered. By introducing a novel Lyapunov–Krasovskii (L–K) functional and utilizing second order reciprocal convex combination technique and Finsler lemma, an improved delay-dependent stability criteria is derived in terms of linear matrix inequalities (LMIs). The information about the time-varying delays and their upper bounds are fully used in the L–K functional. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]