基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据

针对一类存在泛数有界不确性的区间变时滞线性系统, 利用Lyapunov-Krasovskii (L-K) 泛函方法并结合线性矩阵不等式(LMI) 技术建立一种新的保守性更低的鲁棒稳定性判据. 首先基于时滞分割方法将时滞区间均分成N 等分, 针对不同的子区间构造合适的L-K 泛函; 然后在各自的分割区间采用保守性较小的积分不等式处理泛函沿时间的导数, 基于凸组合技术建立了LMI 形式的时滞相关稳定性新判据; 最后通过数值实例验证了结论的有效性.

     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays

This paper deals with the robust stability problem of uncertain stochastic neural networks of neutral-type with interval time-varying delays. The uncertainties under consideration are norm-bounded, and the delay is assumed to be time-varying and belongs to a given interval. By using the Lyapunov-Krasovskill functional method and the linear matrix inequality (LMI) technique, the novel stability criteria are derived in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed criteria.     

具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

研究一类具有非线性扰动的时变时滞中立型系统鲁棒稳定性问题。基于直接Lyapunov Krasovskii泛函并结合自由权矩阵方法的分析方法,建立了线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关稳定性判据。与以往方法不同,在处理泛函导数时,该方法不包含任何模型变换和涉及交叉项的处理,只是通过引入相关项自由权矩阵,充分考虑各项之间的相互关系,降低了结论的保守性。最后,利用Matlab的LMI工具箱进行了的数值仿真, 算例仿真表明所提出的判据的有效性。     

Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties

In this paper, we study the delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes linear fractional norm-bounded uncertainty. Based on the new Lyapunov–Krasovskii functional, some inequality techniques and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, some numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

基于增广泛函的混合时滞区间神经网络的鲁棒稳定性

本文针对一类带有混合时变时滞 (离散和分布时滞)的区间递归神经网络进行了全局鲁棒稳定性研究.与之前的处理方法不同,在本文中通过使用一种新型的增广Lyapunov-Krasovskii泛函,从而得到了一类新颖的关于区间递归神经网络的时滞依赖全局鲁棒稳定性判据.在新的增广泛函中,由于首次使用了带有激活函数的积分项,系统状态和激活函数之间的关系将被更好地表示出来.因此,本文提出的判据具有更小的保守性.同时,在本文提出的判据中,放松了时变时滞变化率必须小于1的限制.仿真结果进一步证明了本文结果的有效性.     

具有时变时滞的Lurie系统时滞依赖绝对稳定性新判据

考虑了一类具有时变时滞和范数有界不确定的Lurie控制系统绝对稳定性分析问题. 通过选取一个新的Lyapunov-Krasovskii泛函将整个时滞区间分为两段, 每段区间上定义了不同的能量函数. 并给出了由LMI描述的新的时滞依赖鲁棒绝对稳定性判据.     

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

Stability analysis of linear systems with an interval time-varying delay – A delay-range-partition approach

In this paper, the stability analysis problem of linear systems with an interval time-varying delay is investigated. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, which includes more information of the delay’s range and the delay’s derivative. Secondly, based on two improved integral inequalities which are less conservative than Jensen’s integral inequalities, a delay-range-partition (DRP) approach is proposed to estimate the upper bound of the derivative of the augmented Lyapunov-Krasovskii functional. Then, less conservative stability criteria in the form of linear matrix inequality (LMI) are established no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given, and their results are compared with the existing results.     

New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay

This paper focuses on the stability problem for uncertain T-S fuzzy systems with interval time-varying delay. The system uncertainties are assumed to be time-varying and norm-bounded. The time-varying delay is considered as either being differentiable uniformly bounded with delay-derivative bounded by constant interval, or being fast-varying case with no restrictions on the delay derivative. Since we employ a novel Lyapunov-Krasovskii functional (LKF) which contains the information on the time-varying delay, and estimate the upper bound of its derivative less conservatively and adopt the convex optimization approach, some less conservative delay-derivative-dependent stability conditions are obtained in terms of linear matrix inequalities (LMIs), without using any free weighting matrix. These conditions are derived that depends on both the upper and lower bounds of the delay derivatives. Finally, some numerical examples are given to demonstrate the effectiveness and reduced conservatism of the proposed method.     

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay.Some Lyapunov-Krasovskii functionals are constructed and the linear matrix inequality(LMI)approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence,uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties.By using Leihniz-Newton formula,free weighting matrices are employed to express this relationship,which implies that the new criteria are less conservative than existing ones.Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

Improved robust stability criteria for a class of Lur'e systems with interval time-varying delays and sector-bounded nonlinearity

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.     

经过一种PTVD补偿的带有快变中立型时滞的系统的时滞依赖稳定性

研究了一类带有时变时滞的线性中立型系统的稳定性, 其中中立型项中的时滞包括一类快变时滞(即, 时滞导数大于1). 目前, 还没有文献考虑带有这种带有快变中立型时滞的系统. 通过使用新的Lyapunov-Krasovskii泛函和带有时滞的多项式(PTVD)补偿技术, 对于此类系统提出了具有更少保守性的时滞依赖稳定性判据. 通过使用新的泛函可以实现处理快变时滞的目的. 同时, 通过使用PTVD补偿技术, 可以在判据中引入一些有用的元素. 而在之前的结果中, 当估计Lyapunov-Krasovskii泛函的上界时, 这些元素通常是被忽略的. 一个数值例子将被提供来验证所得到结果的有效性.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

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.     

时变滞后Lurie型系统的改进稳定性准则

In this technical note, we present a new stability analysis procedure for ascertaining the delay-dependent stability of a class of Lurie systems with time-varying delay and sector-bounded nonlinearity using Lyapunov-Krasovskii (LK) functional approach. The proposed analysis, owing to the candidate LK functional and tighter bounding of its time-derivative, yields less conservative absolute and robust stability criteria for nominal and uncertain systems respectively. The effectiveness of the proposed criteria over some of the recently reported results is demonstrated using a numerical example.     

Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term

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.