随机时滞系统的时滞相关无源控制

研究随机时滞系统的时滞相关无源性分析和控制问题. 利用Lyapunov-Krasovskii方法和松弛矩阵方法, 得到时滞相关的无源性条件. 基于该条件设计时滞相关的随机无源控制器. 文中的结果以线性矩阵不等式(Linear matrix inequalities, LMIs)表示, 可以利用标准的凸优化算法进行有效求解. 通过一个数值例子说明本文方法的有效性.     

线性时滞系统的时滞相关无源控制

讨论了线性时滞系统的时滞相关无源性及无源控制问题.首先,建立了一个基于二次型项的积分不等式.然后,利用这一不等式,采用Lyapunov_Krasovskii泛函方法,获得了系统基于线性矩阵不等式(LMI)的时滞相关无源条件,不必对系统进行模型变换.利用这一条件,给出了无记忆状态反馈无源控制器的设计方法.最后,用一个数值例子说明了该方法所得结果较已有文献具有较小的保守性.     

时滞T-S模糊系统的无源控制器设计

针对时滞T-S模糊系统, 给出了使得系统无源的状态反馈控制器存在的充分条件, 与现有结果相比保守性更小. 在此基础上, 给出了基于观测器的无源控制器与动态输出反馈无源控制器存在的充分条件. 控制器的设计方法都归结为求解一组线性矩阵不等式(Linear matrix inequality, LMI). 最后通过仿真例子, 说明所给设计方法的有效性.     

时变时滞不确定性神经网络的被动性准则

研究具有时变时滞不确定性神经网络的被动性问题。通过构造适当的Lyapunov泛函并利用一些分析技巧,给出一个新的条件,以确保与时变延迟的不确定性神经网络的被动性。被动条件以线性矩阵不等式(LMI)表示,可以很容易地通过有效内点算法进行求解。通过一个数例证明了该方法的有效性。     

时滞关联大系统基于分散控制的无源性

无源性不仅是系统的一个重要性质,而且是控制一个系统的重要途径.本文基于分散控制方法研究了关联大系统的无源性.利用Lyapunov-Krasovskii泛函方法和Hamilton函数方法,通过求解线性矩阵不等式(LMIs)得到了分散无源控制器的显式表达.所得到的新的无源性判据和无源控制器的参数是与时滞相关的.当关联时滞已知时,这些新结果的条件易于用Matlab中的LMI工具箱进行验证,因而控制器的设计也容易实现.最后用数值例子说明了所得到定理的有效性和无源控制器的设计过程.     

线性不确定广义时滞系统的鲁棒无源滤波器设计

研究一类线性不确定广义时滞系统的鲁棒无源滤波器设计问题．系统中所含的不确定性假设是未知且范数有界的．利用线性矩阵不等式方法和Lyapunov函数方法相结合,给出了广义滤波增广系统时滞独立的鲁棒无源滤波器的存在条件．设计目标是对所有的不确定性,滤波增广系统是正则、稳定、无脉冲的,且满足所提的无源滤波性能指标．所提的滤波器设计问题可转化为标准的线性矩阵不等式的求解问题,并可推广到多时滞情况．数值例子验证了设计方法的可行性．     

时滞系统时滞相关型稳定性准则

针对常数时滞线性系统的稳定性问题,基于一个适当形式的Lyapunov-Krasovskii泛函,通过利用一个积分不等式,采用时滞分解方法,以线性矩阵不等式的形式给出了时滞系统的时滞相关型稳定性准则.与现有的时滞相关型稳定性结果相比较,所得到的结果具有保守性更好,结构更加简单,且不合有任何多余的矩阵变量等特点,并从理论上进行了严格的证明,解决了现有的稳定性结果绝大多数只是从数值例子说明其有效性的问题.示例说明了所得结果的有效性.     

时滞神经网络的全局渐近稳定性分析

研究一类具有时滞的细胞神经网络的稳定性问题,利用Lyapunov—Krasovskii泛函的方法,给出时滞相关的稳定性判据。稳定性判据是以线性矩阵不等式的形式给出,可以很容易得出时滞的上界。在得到时滞相关的稳定性判据的同时也可以得到时滞无关的稳定性判据。数值算例说明其结果的优越性。     

连续分布时滞Cohen-Grossberg神经网络渐近稳定性准则

通过选取一个新颖的Lyapunov-Krasovskii泛函和引入所考虑系统的等价描述系统, 讨论了具有时变和连续分布时滞Cohen-Grossberg神经网络的渐近稳定性问题. 在变时滞导函数有上界时, 给出能判定系统是渐近稳定时滞相关的充分性条件. 该条件以线性矩阵不等式形式给出, 易于用MATLAB工具箱LMI进行检验. 最后, 数值例子说明了所得结论的有效性.     

A delay-dependent passivity criterion of linear neutral delay systems

The problem of delay-dependent stability and passivity for linear neutral systems is discussed. By constructing a novel type Lyapunov-krasovskii functional, a new delay-dependent passivity criterion is presented in terms of linear matrix inequalities （LMIs）. Model transformation, bounding for cross terms and selecting free weighting matrices [12-14] are not required in the arguments. Numerical examples show that the proposed criteria are available and less conservative than existing results .     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay

This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results. Supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z183), China Postdoctoral Sciencer Foundation (Grant No. 20080431150), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801451096)     

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.     

Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

In this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.     

New results on passivity analysis of uncertain neural networks with time-varying delays

In this paper, the passivity problem is investigated for a class of uncertain neural networks with generalized activation functions. By employing an appropriate Lyapunov–Krasovskii functional, a new delay-dependent criterion for the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.     

New robust exponential stability analysis for uncertain neural networks with time-varying delay

In this paper, the global robust exponential stability is considered for a class of neural networks with parametric uncer-tainties and time-varying delay. By using Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional, some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are presented to show the effectiveness of the proposed method.     

New delay-dependent global asymptotic stability condition for Hopfield neural networks with time-varying delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.     

Stability analysis for recurrent neural networks with time-varying delay

This paper is concerned with the stability analysis for static recurrent neural networks （RNNs） with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities （LMIs）, the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.