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。     

具有状态时滞的切换随机系统的指数稳定条件

考虑由具有状态时滞的线性It(o)随机子系统构成的切换系统,基于多Lyapunov泛函方法研究切换与时滞对于稳定性的共同影响,并以此建立均方指数稳定条件.在均方意义下噪声对于稳定性的影响基本是负面的,因此构造一类形式较为一般的Lyapunov泛函并运用噪声的统计特性于其解析过程中,以减少噪声所引起的保守性.最后,通过一个仿真算例描述切换与时滞的相互制约关系表明了所提出方法的有效性.     

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Lurie时滞系统绝对稳定性分析

研究了不确定Lurie时滞系统的绝对稳定问题。通过构造适当的Lyapunov泛函、引入一些自由权矩阵和充分考虑时滞导数的上限信息,得到了基于LMIs(线性矩阵不等式)形式的时滞相关绝对稳定性新准则,两个数值例子验证了所得结论的有效性和更弱保守性。     

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.     

考虑通信时滞和采样周期的电力系统负荷频率控制

针对电力系统负荷频率稳定控制问题,本文提出了一种时滞/采样相关的离散负荷频率控制(LFC)方案.首先,考虑通信网络传输时滞和反馈信号采样周期对系统的影响,建立闭环电力系统LFC模型.然后,基于建立的LFC模型,利用双边闭环Lyapunov泛函和LMI技术,提出了低保守性的时滞/采样相关稳定准则和控制器设计方法,确保所提控制方案能在一个较大的通信时滞和采样周期条件下保持电力系统稳定运行.最后,通过单区域和三区域电力系统验证所提方法的有效性.仿真结果表明,所设计LFC方案比现有其他LFC方案的控制性能更佳,鲁棒性更强,并且能在一定大小的通信时滞条件下提升电力系统的动态性能.     

改进的时变时滞不确定离散系统的鲁棒稳定性分析

研究了一类具有区间时变时滞的不确定离散时间系统的鲁棒稳定性问题.首先,将时滞区间分成两个子区间,在不同的子区间上通过构造不同的Lyapunov泛函,再结合一个更紧的不等式,在没有忽略任何有用项的前提下,得到了基于线性矩阵不等式形式的时滞相关的稳定性判据.证明过程既没有利用模型变换也没有引进自由权矩阵,降低了结论的保守性和计算量.数值算例说明了该方法的有效性.     

一类具有扇区非线性的时变时滞系统的绝对稳定性

讨论一类具有扇区非线性的时变时滞系统的绝对稳定性问题.基于时滞分段的思想,构造一种新的Lyapunov 泛函,进一步应用自由权矩阵结合积分不等式方法,并充分考虑时变时滞和时滞上界之间的关系,得到了基于LMI的具有更低保守性的时滞相关绝对稳定条件.最后,数值实例表明所提方法的有效性和相比已有结果的优越性.     

多时变状态和控制时滞系统的绝对稳定性

研究了具有多时变状态和控制时滞的Lurie控制系统基于线性矩阵不等式(LMI)的绝对稳定性条件.首先,构造了关于Lyapunov泛函中正定矩阵和积分项系数等自由参数的LMI,获得了系统时滞无关绝对稳定条件.进一步引入自由权矩阵来表示牛顿-莱布尼兹公式中各项的相互关系,得到了系统绝对稳定的时滞相关条件.最后,通过一个实例阐述了本文方法的有效性和相比已有结果的优越性.     

基于划分时滞区间的一类Cohen-Grossberg神经网络的鲁棒稳定性

研究一类具有时变时滞及参数不确性的Cohen-Grossberg神经网络的鲁棒稳定性问题.应用划分时滞区间的思想构造了一个新的Lyapunov泛函,并以线性矩阵不等式的形式给出了平衡点全局鲁棒稳定性判据,新判据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所得结论的有效性.     

Novel delay‐derivative‐dependent stability criteria using new bounding techniques

This paper studies the stability of linear systems with interval time‐varying delays. By constructing a new Lyapunov–Krasovskii functional, two delay‐derivative‐dependent stability criteria are formulated by incorporating with two different bounding techniques to estimate some integral terms appearing in the derivative of the Lyapunov–Krasovskii functional. The first stability criterion is derived by using a generalized integral inequality, and the second stability criterion is obtained by employing a reciprocally convex approach. When applying these two stability criteria to check the stability of a linear system with an interval time‐varying delay, it is shown through some numerical examples that the first stability criterion can provide a larger upper bound of the time‐varying delay than the second stability criterion. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

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.     

Delay‐Dependent Stability Criterion for Discrete‐Time Systems with Time‐Varying Delays

The stability analysis problem is considered for linear discrete‐time systems with time‐varying delays. A novel summation inequality is proposed, which takes the double summation information of the system state into consideration. The inequality relaxes the recently proposed discrete Wirtinger inequality and its improved version. Based on construction of a suitable Lyapunov‐Krasovskii functional and the novel summation inequality, an improved delay‐dependent stability criterion for asymptotic stability of the systems is derived in terms of linear matrix inequalities. Numerical examples are given to demonstrate the advantages of the proposed method.     

Stability analysis of time‐delay systems via Bessel inequality: A quadratic separation approach

In this paper, new sufficient stability conditions for the asymptotic stability of time‐delay systems are presented using the quadratic separation approach. The time‐delay system is modeled as an interconnected closed‐loop system involving a linear transformation and delay‐dependent functions, representing the uncertainties brought by the delay. Those complex‐valued functions are then embedded into adequate norm‐bounded uncertainties, which lead to several stability results. The novelty of this approach relies on the introduction of new dedicated functions that are built in accordance to the Bessel inequality. They allow us to model the system as an uncertain feedback system and to control the accuracy of the inequality. Then, a sequence of linear matrix inequality conditions is proposed, which tends to the analytical bounds for both delay‐dependent stability and delay range stability, at least on examples.     

Improved results for linear discrete-time systems with an interval time-varying input delay

This paper addresses the problem of delay-dependent stability analysis and controller synthesis for a discrete-time system with an interval time-varying input delay. By dividing delay interval into multiple parts and constructing a novel piecewise Lyapunov–Krasovskii functional, an improved delay-partitioning-dependent stability criterion and a stabilisation criterion are obtained in terms of matrix inequalities. Compared with some existing results, since a tighter bounding inequality is employed to deal with the integral items, our results depend on less number of linear matrix inequality scalar decision variables while obtaining same or better allowable upper delay bound. Numerical examples show the effectiveness of the proposed method.     

短时滞的网络控制系统稳定性分析

针对具有时变传输时滞和间隔的网络控制系统(Networked Control Systems,NCSs)进行分析,基于传输时滞及输入时滞构建一种新的依赖于时间的非连续的Lyapunov泛函,提出新的稳定性准则.考虑零阶保持器更新时间在两个有效采样时间范围内,结合缩放方法及凸优化技术,最后通过线性矩阵不等式计算,得到新的...     

具有时滞的不确定鲁里叶控制系统的绝对鲁棒稳定性

讨论了具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定性问题,应用Bellman-Gronwell不等式和Lyapunov泛函方法研究了不确定鲁里叶控制系统的鲁棒绝对稳定性并给出了系统的滞相关稳定和时滞无关稳定的充分判据,运用这些条件可以直接估计具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定界和时滞界。     

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.     

Stability of a class of switched positive linear time‐delay systems

This paper addresses the problem of stability for a class of switched positive linear time‐delay systems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co‐positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co‐positive type Lyapunov–Krasovskii functional to the common co‐positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd.