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This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur'e system with the application of fractal interpolation based image encryption. The variable-order fractional Lur'e system is modeled into fractional order Chua's circuit model with short memory. The synchronization is achieved using event-triggered impulsive control and short memory for chaotic Lur'e systems, employing linear matrix inequalities. The variable-order fractional Chua's circuit systems successfully accomplish their synchronization using both impulsive and event-triggered impulsive control. Furthermore, fractal interpolation function (with function scalings) is applied to reconstruct the chaotic attractors. The Riemann-Liouville variable-order fractional calculus of diverse fractal functions is also investigated in connection with the study on variable-order fractional systems. The interpolated sequence, along with the Arnold transform, modified Fisher Yates algorithm, and additive diffusion, is utilized to propose an image encryption algorithm. Various statistical analyses are conducted to assess the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua's circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm's robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security. [ABSTRACT FROM AUTHOR]

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 central concern of this paper is to study leader‐following quasi‐bipartite synchronisation of a multiple inertial signed neural networks with varying time‐delay by utilising distributed event‐triggered impulsive control scheme, where connections between adjacent nodes of the neural networks either positive or negative. The second‐order neural networks, called inertial neural networks, can be transformed into differential equations of first‐order by implementing suitable variable substitution. Under certain hypothesis about the node dynamics, signed graph theory and balanced topology of networks, some conditions are derived in terms of lower‐dimensional linear matrix inequalities (LMIs) to achieve leader‐following quasi‐bipartite synchronisation. In addition, a basic algebraic condition is derived to estimate the theoretical upper bound for the error node. Finally, some numerical simulations are provided to illustrate the correctness of the theoretical results. [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]

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]

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 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]

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 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 deals with the problem of robust $$H_{\infty }$$ synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov-Krasovskii (L-K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur'e system with a guaranteed $$H_{\infty }$$ performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to $$H_{\infty }$$ norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua's circuit and neural networks. [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, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov-Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our 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 studies the problem of non-fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time-varying coupling delays. By constructing a new Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability-distribution-dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non-fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods. [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]

In this paper, we extensively study the analysis of complete stability of complex-valued neural networks with time delay and impulsive effects. Using stability theory, impulsive effects and by constructing appropriate Lyapunov-Krasovskii functional, some sufficient conditions for the existence and complete stability of complex-valued neural networks with time delay and impulsive effects are derived in the form of complex-valued linear matrix inequality (LMIs) as well as real-valued LMIs. Finally, four numerical examples are given to establish the effectiveness of our theoretical results via standard numerical software. [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]

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]

In this paper, we made an effort to investigate the passivity and passification of memristor-based complex-valued recurrent neural networks (MCVNNs) with interval time-varying delays. By constructing proper Lyapunov-Krasovskii functional and using the characteristic function method, passivity conditions are derived in terms of linear matrix inequalities (LMIs). Then, based on the derived passivity condition, the desired feedback controller is designed, which ensures the MCVNNs with interval time-varying delays to be passive. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This article deals with the state estimation problem of memristor-based recurrent neural networks (MRNNs) with time-varying delay based on passivity theory. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delay, the dynamics of the estimation error is passive from the control input to the output error. Based on the Lyapunov-Krasovskii functional (LKF) involving proper triple integral terms, convex combination technique, and reciprocal convex technique, a delay-dependent state estimation of MRNNs with time-varying delay is established in terms of linear matrix inequalities (LMIs). The information about the neuron activation functions and lower bound of the time-varying delays is fully used in the LKF. Then, the desired estimator gain matrix is accomplished by solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theoretical results. © 2013 Wiley Periodicals, Inc. Complexity 19: 32-43, 2014 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the stability analysis problem is investigated for delayed neural networks with mixed time-varying delays, impulsive control and Markovian jumping parameters. The mixed time-varying delays include leakage, discrete and distributed time-varying delays. Sufficient conditions for the global exponential stability in the mean square are derived by using Lyapunov–Krasovskii functional having triple integral terms and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical softwares. Finally, three numerical examples and simulations are given to demonstrate the usefulness and effectiveness of the presented results. [Copyright &y& Elsevier]

In this paper, a class of stationary oscillation of interval fuzzy cellular neural networks (FCNNs) with mixed delays under impulsive perturbations are considered. Mixed delays include discrete time-varying delays and unbounded distributed delays. By establishing a simple Lyapunov function, using impulsive differential inequality techniques and LMI techniques, some new sufficient criteria are obtained to ensure the existence, uniqueness and global exponential stability of stationary oscillation of interval FCNNs. The obtained results can be checked easily by the LMI control toolbox in MATLAB. Moreover, the results obtained in this paper are useful in the application and design of FCNNs, since the sufficient criteria are simple and easy to check in practice. A numerical example is given to illustrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

This paper considers existence, uniqueness, and the global asymptotic stability for a class of High-order Hopfield neural networks with mixed delays and impulses. The mixed delays include constant delay in the leakage term (i.e., "leakage delay") and time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-dependent sufficient conditions are presented for the global asymptotic stability of the equilibrium point of the considered neural networks. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the applicability of the result. [ABSTRACT FROM AUTHOR]

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of delay-dependent global robust asymptotic stability of uncertain switched Hopfield neural networks (USHNNs) with discrete interval and distributed time-varying delays and time delay in the leakage term. Some Lyapunov--Krasovskii functionals are constructed and the linear matrix inequality (LMI) approach are employed to derive some delay-dependent global robust stability criteria which guarantee the global robust asymptotic stability of the equilibrium point for all admissible parametric uncertainties. The proposed results that do not require the boundedness, differentiability, and monotonicity of the activation functions. Moreover, the stability behavior of USHNNs is very sensitive to the time delay in the leakage term. It can be easily checked via the LMI control toolbox in Matlab. In the absence of leakage delay, the results obtained are also new results. Finally, nine numerical examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the exponential synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov—Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequalities, 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]

• The effect of synchronisation on the master-slave NNs with time delay is examined. • The NN's chaotic attractor is reconstructed using the fractal interpolation. • Reconstructed chaotic sequence is applied in image encryption. • Image encryption is carried out using RSA algorithm. • Various statistical measures are used to verify the efficacy. This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors. Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the stability problem for a class of dynamical systems with leakage delay and nonlinear perturbations based on linear matrix inequality (LMI) approach. Some sufficient conditions which are dependent on the leakage delay are derived to ensure the global asymptotic stability by using Lyapunov–Krasovskii functional method and free weighting matrix technique. Two examples and their simulations are given to show the effectiveness and advantage of the present results. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov–Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results. [Copyright &y& Elsevier]