改进的区间变时滞基因调控网络稳定性准则

为提高带区间变时滞基因调控网络的全局稳定性,利用李亚普诺夫泛函、线性矩阵不等式方法和新的积分不等式,得到一类改进基因调控网络的全局渐近稳定性判定条件。该稳定性准则不仅考虑时滞的时变因素,而且考虑时滞的上界和下界,由于采用新的积分不等式,使得这些结果具有更小的保守性且参数较少,对人工设计基因芯片可提供一定的参考。通过2个数值实例证明了理论结果的有效性。     

时滞基因调控网络的全局渐进稳定性分析

针对一类时滞基因调控网络的全局渐进稳定性进行了研究, 利用Lyapunov泛函、线性矩阵不等式（LMIs）和自由权值矩阵（free-weighting matrices）技术, 得到了一些新的时滞相关的基因调控网络稳定性充分条件。通过在Lyapunov泛函中使用辅助矩阵E, 并对调控函数条件一般化, 取得的结果具有较少的保守型和更广的适用性。该结果为人工设计基因芯片提供一定的参考作用。仿真示例进一步验证了结论的有效性。     

带有时变时滞的切换基因调控网络的稳定性

研究了带有时变时滞的切换基因调控网络的稳定性问题。和现有关于切换基因调控网络结果不同的是,切换基因调控网络包括稳定子系统和不稳定子系统。利用平均驻时方法和线性矩阵不等式技术,得到了带有时变时滞的切换基因调控网络指数稳定的判据。最后的仿真实例验证了结果的有效性。     

带加性时变时滞的不确定神经网络鲁棒散耗性研究

针对加性时变时滞不确定神经网络的时滞相关鲁棒耗散性问题,提出了一种更一般化的激活函数。与以往研究不同,充分考虑了关于神经元激活函数和加性时变时滞的充分信息,通过使用一些新的积分项构造合适的Lyapunov-Krasovskii泛函（LKF）,并利用新生成的单积分不等式来计算其导数,包括延森不等式和维特林积分不等式的特殊情形。利用线性矩阵不等式（LMI）技术建立了一个新的时滞相关的不守恒全局渐近稳定性和耗散准则。最终通过计算和数值仿真验证了所提理论的有效性。     

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.     

具有多个时滞的积分时滞系统的稳定性分析

首先,针对具有多个时滞的积分时滞系统,建立新的基于线性矩阵不等式的稳定性条件.该条件与正整数k有关,给出$k=1$时该条件与现有结果间的关系.该关系表明所提出条件在$k\geqslant2$时的保守性比现有结果小;然后,基于所提出的稳定性条件,进一步研究具有参数不确定性的积分时滞系统的鲁棒稳定性问题,建立基于线性矩阵不等式的充分条件;最后,利用所提出方法,研究具有多个离散时滞和分布时滞的积分时滞系统的稳定性问题.数值算例结果表明了所提出稳定性判据的有效性.     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

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.     

时滞乘积型Lyapunov泛函的时变时滞系统稳定性新判据

应用新的Lyapunov泛函研究时变时滞系统的渐近稳定性问题.首先,基于Bessel-Legendre积分不等式和改进的自由矩阵积分不等式,提出两个新的时滞乘积型Lyapunov泛函,其充分利用时滞$d(t)$与二次型函数的乘积信息以及时滞$h-d(t)$与二次型函数的乘积信息;然后,采用Bessel-Legendre积分不等式和改进的逆凸组合方法估计时滞乘积型Lyapunov泛函导数的积分项,得到两个低保守性的时滞相关稳定性判据;最后,通过两个数值算例进行验证,结果表明,与最近相关方法相比,所提出方法可获得更大的允许时滞上界,进一步表明了所提出方法的可行性和低保守性.     

不确定线性系统新的稳定性准则

研究了带有区间时滞的不确定系统的稳定性问题。通过采用时滞分割法,把时滞区间分割成任意两小段,并构造恰当的Lyapunov函数,利用积分不等式,得到了新的时滞相关的稳定性准则。通过数值例子验证了结果的有效性。     

Finite-time stability of neutral-type neural networks with random time-varying delays

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov–Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.     

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma(BRL)for Markovian jump linear systems with interval time-varying delays.By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method,the free weighting matrix method,the convex combination method and the delay decomposition approach integratedly,some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.     

时滞随机系统的稳定性分析

针对一类时变时滞随机系统,研究其渐近稳定性问题。通过构造李亚普诺夫函数,引用适当的自由权矩阵,利用积分等式、积分不等式,给出系统渐进稳定的时滞相关的充分条件,其结果用线性矩阵不等式形式表示.用数值算例说明方法的有效性。     

Stability analysis of systems via a new double free-matrix-based integral inequality with interval time-varying delay

ABSTRACT

This paper investigates the problem of delay-dependent stability analysis for systems with interval time-varying delay. By means of a new double free-matrix-based integral inequality and augmented Lyapunov–Krasovskii functionals containing as much information of time-varying delay as possible, a new stability criterion for systems is established. Firstly, by a double integral term two-step estimation approach and combined with single free-matrix-based integral inequalities, a stability criteria is presented. Then, compared with the double integral term two-step estimation approach, the proposed new double free-matrix-based integral inequality with more related time delays has potential to lead to a criterion with less conservatism. Finally, the validity of the presented method is demonstrated by two numerical examples.     

不确定线性多时变时滞系统的时滞相关鲁棒控制

提出一种积分不等式新方法，讨论不确定线性多时变时滞系统的鲁棒稳定性以及鲁棒稳定化问题，首先利用Park不等式建立了基于二次型项的积分不等式，利用这一不等式获得了系统基于LMI的时滞相关、时滞导数相关鲁棒稳定条件；然后利用这一条件给出了时滞状态反馈控制器的一种新的设计方法，数值例子说明了所得结论具有较小的保守性。     

On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay

 This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.     

Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach

This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.     

Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays

This paper is concerned with robust stabilization for a class of T-S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov-Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.     

Delay-dependent approach to robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties

A delay-dependent approach to robust H _∞ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with H _∞ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust H _∞ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.     

Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality

This paper investigates the stochastic stability problem for a class of neutral-type Markov jump neural networks with additive time-varying delays. Firstly, to derive a tighter lower bound of the reciprocally convex quadratic terms, a new reciprocally convex combination inequality is established by using parameters transformation approach. Secondly, by fully considering the peculiarity of various time-varying delays and Markov jumping parameters, an eligible stochastic Lyapunov–Krasovskii functional is constructed. Then, by employing the new reciprocally convex combination inequality and other analytical techniques, some novel stability criteria are provided in the forms of linear matrix inequalities. Finally, four illustrated examples are given to verify the effectiveness and feasibility of the proposed methods.