Novel stability and stabilization criteria for Takagi-Sugeno fuzzy time-delay systems

We study the problems of stability and stabilization for Takagi-Sugeno(T-S) fuzzy time-delay systems.First,by constructing a less-redundant Lyapunov-Krasovskii function and introducing a useful inequality,an innovative stability criterion is obtained,which gives a significant improvement on the performance.Compared with the exiting references,our result can use fewer unknown variables and get better results.Furthermore,based on the derived stability criteria,a new stabilization condition is developed,in which the controller gain and the maximum allowable delay bound can be obtained simultaneously.The conditions are all derived in the form of linear matrix inequality,which are easy to verify.Finally,numerical examples are given to show the effectiveness of the proposed methods.     

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.     

具连续分布时滞的抛物型系统的指数镇定

针对一类具分布时滞的抛物型控制系统，提出一种新的镇定设计方法.利用推广的向量Hanalay 微分不等式、Dini导数、结合Green公式及不等式分析技术，在线性反馈控制律的作用下，导出了具分布时滞的抛物型控制系统的镇定的新判据.该镇定性条件不依赖于时滞.最后给了一个算例说明所得结果的可行性.此外，该方法一个明显的优点是所得的镇定性条件容易验证，因而便于应用. 关键词： 抛物型系统 Dini导数 分布时滞 全局指数镇定     

Stochastic finite-time stability of reaction-diffusion Cohen–Grossberg neural networks with time-varying delays

This paper investigates the problem of the stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time varying delays using the Dirichlet boundary condition. The concept of finite-time stability for the system is first derived by using the stochastic conditions. By constructing a new Lyapunov–Krasovskii functional and utilizing Jensen’s inequality, Wirtinger’s type inequality technique, the Gronwall inequality and the linear matrix inequality (LMI) frame work, conditions are obtained which guarantee the stochastically finite-time stability of Cohen–Grossberg neural networks. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi--Sugeno (T--S) fuzzy model is employed to represent the chaotic system dynamics. To acquire the good performance and produce less conservative analysis result, a new parameter-dependent Lyapunov--Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.     

Stabilizability of discrete chaotic systems via unified impulsive control

This Letter is concerned with the asymptotical stabilization problem of discrete chaotic systems by using a novel unified impulsive control scheme. Sufficient conditions for asymptotical stability of the impulsive controlled discrete systems are obtained by means of the Lyapunov stability theory and algebraic inequality techniques. Finally, numerical simulations on the Hénon and Ushio discrete chaotic systems are presented to illustrate the effectiveness and usefulness of the unified impulsive control scheme.     

Non-fragile synchronization of genetic regulatory networks with randomly occurring controller gain fluctuation

This study examines the non-fragile synchronization of genetic regulatory networks (GRNs) with time-varying delays. Genetic regulatory network is formulated and sufficient conditions are derived to guarantee its synchronization based on master-slave system approach. The non-fragile observer based feedback controller gains are assumed to have the random fluctuations, two different types of uncertainties which perturb the gains are taken into account. By constructing a suitable Lyapunov-Krasovskii stability theory together with linear matrix inequality (LMI) approach we derived the delay-dependent criteria to ensure the asymptotic stability of the error system, which guarantees the master system synchronize with the slave system. The expressions for the non-fragile controller can be obtained by solving a set of LMIs using standard softwares. Finally, some numerical examples are included to show that the proposed method is less conservative than existing ones.     

Global exponential stability of reaction diffusion neural networks with discrete and distributed time-varying delays

This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays.By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities.The obtained results are dependent on the size of the time-varying delays and the measure of the space,which are usually less conservative than delay-independent and space-independent ones.These results are easy to check,and improve upon the existing stability results.Some remarks are given to show the advantages of the obtained results over the previous results.A numerical example has been presented to show the usefulness of the derived linear matrix inequality(LMI)-based stability conditions.     

Finite time decentralized event-triggered communication scheme for neutral-type Markovian jump neural networks with time varying delays

The objective of this paper is to analyze the finite time problem of a class of neutral-type Markovian jump neural networks with time varying delays and parametric uncertainties using decentralized event-triggered communication scheme. We present a methodology for designing decentralized event-triggered, which utilize only locally available information, for determining the time instants of transmission from the sensors to the central controller. Based on the Lyapunov function with inequality techniques like reciprocal convex combination method, some sufficient conditions are derived to guarantee the finite-time stability of the considered neural networks. Furthermore, the decentralized event-triggered scheme combined with state feedback controller and is designed to solve the finite time stability. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones.     

Improved Conditions for Global Asymptotic Stability of Cohen--Grossberg Neural Networks with Time-Varying Delays

The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses. An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.     

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

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.     

Finite-Time Quasi-Synchronization of Two Nonidentical Chaotic Systems via Intermittent Control

This paper investigates the finite-time quasi-synchronization of two nonidentical Lur'e systems with parameter mismatches by using intermittent control. Based on Lyapunov stability theory and some differential inequality techniques, sufficient conditions for finite-time quasi-synchronization are derived and the explicit expression of error level is obtained. Meanwhile, a numerical simulation is given to illustrate the effectiveness of the theoretical results.     

The stability control of fractional order unified chaotic system with sliding mode control theory

This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwall’s inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.     

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach,the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional,some inequality techniques and stochastic stability theory,new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism,which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally,numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.     

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme (the so-called dual-stage impulsive control), some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.     

Synthesized AI LMI-based Criterion for Mechanical Systems

This paper proposes a novel artificial intelligence sythethized controller in the mechanical system which has high speed computation because of the LMI type criterion. The proposed membership functions are adopted and stabilization criterion of the closed-loop T-S fuzzy systems are obtained through a new parametrized LMI (linear matrix) inequality which is rearranged by machine learning membership functions.     

Synchronization control of stochastic delayed neural networks

In this paper, synchronization control of stochastic neural networks with time-varying delays has been considered. A novel control method is given using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system, and thus the drive system synchronize with the response system. Also, the estimation gains can be obtained. With these new and effective methods, synchronization can be achieved. Simulation results are given to verify the theoretical analysis in this paper.     

一种基于特征点跟踪的电子稳像算法

提出一种基于特征点跟踪的稳像算法。该算法从参考帧图像中提取出一组特征点,然后在后续帧中进行基于Kalman滤波的特征点的跟踪,匹配参考帧图像中特征点的坐标和当前图像中基于Kalman滤波修正后得到的特征点的坐标,并通过仿射模型求出位移量及旋转参数,最后进行反向变换,从而得到稳定的视频图像。实验结果表明:该算法稳像效果好,运算复杂度低,且具有较强的鲁棒性。     

Pinning control of weighted general complex dynamical networks with time delay

Time delays commonly exist in the real world. In the present work we consider weighted general complex dynamical networks with time delay, which are undirected and connected. Control of such networks, by applying local feedback injections to a fraction of network nodes, is investigated for both continuous-time and discrete-time cases. Both delay-independent and delay-dependent asymptotical stability criteria for network stabilization are derived. It is also shown that the whole network can be stabilized by controlling only one node. The efficiency of the derived results was illustrated by numerical examples.