Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

New delay-dependent stability criteria for neural networks with time-varying interval delay

The problem of stability analysis of neural networks with time-varying delay in a given range is investigated in this Letter. By introducing a new Lyapunov functional which uses the information on the lower bound of the delay sufficiently and an augmented Lyapunov functional which contains some triple-integral terms, some improved delay-dependent stability criteria are derived using the free-weighting matrices method. Numerical examples are presented to illustrate the less conservatism of the obtained results and the effectiveness of the proposed method.     

An LMI approach to asymptotical stability of multi-delayed neural networks

In this paper, some criteria are derived for global asymptotic stability of a class of neural networks with multiple constant or time-varying delays. Based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach, some delay-independent criteria for neural networks with multiple constant delays and delay-dependent criteria for neural networks with multiple time-varying delays are provided to guarantee global asymptotic stability of these networks. The main results are generalizations of some recent results reported in the literature.     

Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays

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.     

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

In this paper we present a synchronization method for chaotic Lur'e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur'e systems with deadzone nonlinearity. Based on the Lyapunov--Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.     

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno(T-S) fuzzy Hopfield neural networks(FHNNs) with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler’s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.     

An improved impulsive control approach to nonlinear systems with time-varying delays

A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

A new complex network model and convergence dynamics for reputation computation in virtual organizations

In this Letter, a new complex network model is established for reputation computation in virtual organizations, and its dynamics is investigated. Several sufficient conditions have been derived to ensure the global asymptotical stability of the new complex network model by using Lyapunov method and linear matrix inequality (LMI) technique, where the stability means that the reputation degrees of entities can tend to some fixed constants as time evolves. Also, for this new model, some other dynamical phenomena such as bifurcation and chaos synchronization are proposed for our consideration in the future. This may open a new research branch in the area.     

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization(SLS) on a dynamical network with communication delay is investigated.In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.     

Synchronization analysis of singular hybrid coupled networks

In this Letter, singular hybrid coupled systems are introduced to describe complex networks with a special class of constraints. The synchronization problem of singular hybrid coupled systems with time-varying nonlinear perturbation is investigated. A sufficient condition for global synchronization is derived based on the Lyapunov stability theory. The singular system is regular and impulse free. Finally, a numerical example is provided to illustrate the effectiveness of the proposal conditions.     

Lyapunov Functionals and L 1 -Stability for Discrete Velocity Boltzmann Equations

We devise Lyapunov functionals and prove uniform L¹ stability for one-dimensional semilinear hyperbolic systems with quadratic nonlinear source terms. These systems encompass a class of discrete velocity models for the Boltzmann equation. The Lyapunov functional is equivalent to the L¹ distance between two weak solutions and non-increasing in time. They result from computations of two point interactions in the phase space. For certain models with only transversal collisional terms there exist generalizations for three and multi-point interactions.     

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.     

New asymptotic stability criteria for neural networks with time-varying delay

The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delay is investigated. A new class of Lyapunov functional is constructed to derive some new delay-dependent stability criteria.The obtained criterion are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.     

Global stability analysis of fluid flows using sum-of-squares

This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite dimensional Navier-Stokes systems using robust optimization techniques. Crucially, this extension requires only the solution of infinite-dimensional linear eigenvalue problems and finite-dimensional sum-of-squares optimization problems.We further show that subject to minor technical constraints, a general polynomial Lyapunov function is always guaranteed to provide better results than the classical energy methods in determining a lower-bound on the maximum Reynolds number for which a flow is globally stable, if the flow does remain globally stable for Reynolds numbers at least slightly beyond the energy stability limit. Such polynomial functions can be searched for efficiently using the SOS technique we propose.     

Global synchronization in arrays of delayed neural networks with constant and delayed coupling

This Letter investigates the global exponential synchronization in arrays of coupled identical delayed neural networks (DNNs) with constant and delayed coupling. By referring to Lyapunov functional method and Kronecker product technique, some sufficient conditions are derived for global synchronization of such systems. These new synchronization criteria offer some adjustable matrix parameters, which is of important significance in the design and applications of such coupled DNNs, and the results improve and extend the earlier works. Finally, an example is given to illustrate the theoretical results.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Globally exponential multi switching-combination synchronization control of chaotic systems for secure communications

This article introduces the global exponential multi switching combination synchronization (GEMSCS) for three different chaotic systems with known parameters in the master-slave system configuration. The proposed GEMSCS scheme establishes the global exponential stability of the synchronization error at the origin with different combinations of state variables of the two master chaotic systems with the state variables of a slave chaotic system in diverse manners. Consequently, it increases the complexity level of the information signal in secure communications. To study the GEMSCS, an efficient nonlinear control algorithm is designed. The Lyapunov direct theorem is used to accomplish the global exponential stability of the synchronization error at the origin. The stability conditions are derived analytically. To show the effectiveness and advantages of the proposed GEMSCS control approach, two numerical examples are presented. The computer based simulation results are compared with the reported works in the relevant literature. This article also extends the idea of GEMSCS to the secure communication using the chaotic masking technique. Using the GEMSCS strategy, the information signal is recovered at the receiving system with good accuracy and high speed while the parameters of the transmitter and receiver systems mismatch. At the end, some future research problems related to this work are suggested.     

Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag—Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.     

时滞双向联想记忆神经网络的全局稳定性

通过构造一个合适的Lyapunov泛函及应用不等式的分析技巧研究了具有时滞的双向联想记忆 神经网络的平衡点的全局稳定性问题-在对神经元激励函数较宽松的假设条件下（可以不满 足Lipschitz条件），获得了一个新的保证全局渐近稳定性的判定准则-结果可应用于包含非 Lipschitz的一类更加广泛的神经元激励函数的神经网络的设计中- 关键词： Lyapunov泛函 时滞 双向联想记忆神经网络 全局渐近稳定性     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.