具有概率分布时滞的神经网络稳定性新判据

基于概率理论和Lyapunov稳定性理论,研究一类具有概率分布时滞神经网络稳定性问题。通过构造合适的Lyapunov-Krasovskii（LK）泛函,运用Wirtinger不等式和倒凸技术来估计LK泛函导数的上界,得到了确保该类时滞神经网络在均方意义下的全局渐近稳定的新判据。该判据以LMIs形式表出,它不但依赖于时滞的上界,而且依赖于时滞的概率分布。给出两个数值例子,仿真表明所提方法的有效性和较弱的保守性。     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

基于二次分离方法的时变时滞系统稳定性分析

基于二次分离方法研究时变时滞系统的时滞相关稳定性问题.通过引入更为严格的积分二次约束,取得保守性更小的稳定性判据.借鉴时变时滞分解思想,提出基于线性矩阵不等式的改进的稳定性判据.数值算例表明了所提出方法的有效性.     

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.

     

一类区间时变时滞系统的稳定性分析

针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.     

含区间时变时滞的线性不确定系统鲁棒稳定性新判据

研究一类区间时变时滞线性不确定系统的鲁棒稳定性问题.通过引入增广Lyapunov泛函,结合积分不等式方法,导出了区间时变时滞线性系统的时滞相关鲁棒稳定性新判据.与现有方法不同,该方法不涉及自由权矩阵技术和任何模型变换,减少了理论和计算上的复杂性,而且在估计Lyapunov泛函导数的上界时没有忽略某些有用项.数值算例表明,所提出的判据是有效的,具有更低的保守性.     

时变时滞神经网络的时滞相关鲁棒稳定性和耗散性分析

研究时变时滞神经网络的鲁棒稳定性和耗散性问题.充分利用积分项的时滞信息和激励函数条件构造一个合适的增广LK泛函;利用自由矩阵积分不等式处理LK泛函的导数,得到一个低保守性的时滞相关稳定判据;将所获得的结论延伸至神经网络的耗散性分析,并推导出一个确保神经网络严格$(\mathcalX, \mathcalY,\mathcalZ)-\gamma$-耗散的充分条件.最后通过3个数值算例验证了所提出方法的可行性和优越性.     

一类时变时滞系统的稳定性分析

针对时变时滞系统稳定性问题, 在考虑非线性扰动的情况下, 为了降低时变时滞系统稳定性判据的保守性, 以改进的Jensen 不等式, Wirtinger型双重积分不等式以及优化凸组合技术为基础, 构造增广的Lyapunov-Krasovskii 泛函, 得到了新的时滞相关稳定性判据. 最后, 通过数值仿真对比可知, 该稳定性判据具有较小的保守性和良好的鲁棒性.     

基于辅助函数积分不等式的不确定转移率的Markov跳变神经网络的稳定性分析

研究具有区间时变分布时滞和不确定转移率的Markov跳变区间时变时滞神经网络的稳定性问题.通过充分考虑转移概率的性质和不确定区域的特性,用一个有效的技术代替传统的Young''s不等式来约束转移率中的不确定项.同时,利用增广的李雅普诺夫泛函和具有较小保守性的辅助函数积分不等式,给出新的时滞依赖的稳定条件.仿真结果验证了所提出方法的有效性.     

具概率分布变时滞随机系统鲁棒稳定性

本文研究了一类有非线性时变随机时滞的线性不确定系统的鲁棒稳定性．其中时变随机时滞表征为伯努利随机过程,具有已知的概率分布和变化范围．通过构造新泛函,建立了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件,此条件易于用MATLABH2具箱来验证．本文所获得结果的主要特征是稳定性条件依赖时滞的概率分布和时滞导数的上界．同时也证明了允许时变随机时滞的时滞比之传统的确定性时滞有更大的变化范围,因此我们的条件比确定性时滞更为保守．算例表明了文中所提方法的有效性．     

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.     

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.     

Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov-Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.     

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.     

Improved delay-dependent stability criteria for neutral-type systems with time-varying delays: a delayed decomposition approach

This paper discusses the neutral system with time-varying delay. Firstly, by developing a delayed decomposition approach and introducing integral inequality approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz–Newton formula into account. The criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show the less conservatism of our obtained results and the effectiveness of the proposed method.     

New stability criteria for singular systems with time-varying delay and nonlinear perturbations

This paper concerns the stability analysis for singular systems with time-varying delay and nonlinear perturbations. Two cases of time-varying delay, which is differentiable (Case 1) or not differentiable (Case 2), are considered. The considered nonlinear perturbations includes the norm-bounded uncertainties as a special case. Some delay-dependent stability criteria are derived by using a delay decomposition approach. In the delay decomposition approach, the entire delay interval is divided into multiple sub-intervals for which different energy functions are defined for building new Lyapunov–Krasovskii functional. Some numerical and practical examples are given to show the effectiveness and significant improvement of the proposed method.     

一类时滞切换系统的稳定性分析

利用时滞分解和平均驻留时间方法讨论一类时滞切换系统的稳定性问题.定义了更为一般的Lyapunov函数,结合Jensen积分不等式和倒数凸组合技术得到的线性矩阵不等式条件具有更小的保守性和更低的计算复杂性给出的仿真算例进一步验证了所得结果的有效性.     

Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay

This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained 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-interval-dependent robust-stability criteria for neutral stochastic neural networks with polytopic and linear fractional uncertainties

In this paper, the delay-interval-dependent robust stability is studied for a class of neutral stochastic neural networks with time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the upper bound is known and the lower bound is not restricted to zero. For the neural networks under study, the uncertainty includes polytopic uncertainty and linear fractional norm-bounded uncertainty. Sufficient conditions for the stability of the addressed neutral stochastic neural networks with time-varying delays are established by employing the proper Lyapunov–Krasovskii functional, a combination of the stochastic analysis theory, some inequality techniques and new linear matrix inequality (LMI). Finally, three numerical examples are provided to demonstrate less conservatism and effectiveness of the proposed LMI conditions.