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.     

离散时滞Lur’e系统时滞依赖性稳定性判据

本文研究了离散时滞Lur’e系统的绝对稳定性和鲁棒绝对稳定性问题,包含时变时滞和扇形有界约束的非线性.首先,构造了新颖的李雅普诺夫-克拉索夫斯基泛函(Lyapunov-Krasovskii functional, LKF),其中,为了增补时变时滞区间和其他系统状态变量之间的耦合信息, LKF中扩充了一些重要的向量.其次,结合改进的基于自由权重矩阵求和不等式技巧,推导了一些比已有结论保守性更低的绝对和鲁棒绝对稳定性判据.稳定性判据保守性的减小主要归功于改进的LKF和求和不等式技巧.最后,通过几个文献中常用的数值算例的求解仿真来说明本文判据的有效性和先进性.     

改进的时变时滞中立型系统的绝对稳定性判据

研究具有时变时滞和扇区有界非线性的中立型系统的绝对稳定性问题.根据时变时滞分段分析思想,构造一个新的Lyapunov-Krasovskii泛函,得到了一些保守性更小的基于线性矩阵不等式的时滞相关绝对稳定性判据.采用凸组合方法,可以避免忽略Lyapunov-Krasovskii泛函微分中的有用项.数值算例表明了所提出方法的有效性.     

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.     

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.     

区间变时滞不确定线性系统带记忆H∞状态反馈控制

一类存在范数有界不确定性的线性时变时滞系统, 其时变时滞仅给出时滞变化的上下界, 而对时滞变化率未作任何约束. 对于这类区间时变时滞系统, 给出了一种新型的 Lyapunov-Krasovskii 泛函讨论其稳定性, 通过分割平均时滞的方法减小保守性, 得到以线性矩阵不等式(LMI)形式给出的稳定性判据. 最后分析并给出了一种带记忆的 H∞ 状态反馈控制器. 数值实例表明了本文方法的有效性.     

模型相关时变时滞马尔可夫跳变系统低保守稳定性

本文研究了时变时滞与模型相关的随机马尔可夫跳变系统的时滞相关稳定性问题. 通过建立时变时滞与模型相关的系统模型, 构造不同的Lyapunov-Krasovskii函数, 并通过引入改进的积分等式, 以线性矩阵不等式的形式提出了具有较小保守性的时滞依赖稳定性条件. 最后用几个数值算例说明本文结论的有效性及较低的保守性.     

时滞系统稳定性分析和镇定: 一种基于Finsler引理的统一观点

从Finsler引理角度,研究时滞系统的时滞相关稳定性分析和镇定问题,发现自由权矩阵方法是该研究框架的一个特例,阐明引入乘子矩阵对分析时变时滞系统稳定性的必要性,讨论乘子矩阵结构对所得结果保守性的影响,提出一些改进的基于线性矩阵不等式的稳定性判据和镇定控制器设计算法,数值算例表明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.     

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.     

基于新型 Abel 型有限和不等式的时滞系统稳定性判据

针对线性离散时滞系统的时滞相关稳定性问题进行研究,提出一个新的有限和不等式,是Abel型不等式的进一步推广.利用这一不等式和构造适当的Lyapunov-Krasovskii泛函,给出新的离散时滞系统稳定性判别准则,并应用数值例子进行验证.验证结果表明,所提出方法与Abel型不等式方法相比,能够获得更大的允许上界,比用自由权方法使用更少的决策变量,降低了数值计算负担,进一步表明了所得结果的有效性和优越性.     

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.     

一类具有变时滞的Hopfield型神经网络的全局指数稳定性

通过构造适当的Lyapunov函数,利用Halanay不等式和Young不等式,讨论一类具有变时滞的Hopfield型神经网络的全局指数稳定性.在对网络施加两个不同的神经元激励函数的条件下,导出网络全局指数稳定的一个充分条件,得到的充分条件在实际应用中易于验证,且有较小的保守性,因而对网络的应用和设计具有重要意义.最后,一个数值实例进一步验证结果的正确性.     

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。     

Improved stability criteria for linear time-varying systems on time scales

ABSTRACT

In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results.     

New results on stability analysis of singular time-delay systems

This paper deals with the problem of delay-dependent stability analysis for singular systems with a constant time delay. By employing the Jensen inequality and the Wirtinger-based inequality, new delay-dependent stability criteria are developed. Furthermore, in order to obtain less conservative results, a new method of constructing Lyapunov--Krasovskii functionals (LKFs) is used. It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are removed. All the criteria are proposed in terms of strict linear matrix inequalities. Finally, numerical examples are given to demonstrate the less conservatism of the 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.     

Bessel summation inequalities for stability analysis of discrete‐time systems with time‐varying delays

This paper is concerned with the stability analysis problems of discrete‐time systems with time‐varying delays using summation inequalities. In the literature focusing on the Lyapunov‐Krasovskii approach, the Jensen integral/summation inequalities have played important roles to develop less conservative stability criteria and thus have been widely studied. Recently, the Jensen integral inequality was successfully generalized to the Bessel‐Legendre inequalities constructed with arbitrary‐order Legendre polynomials. It was also shown that general inequality contributes to the less conservatism of stability criteria. In the case of discrete‐time systems, however, the Jensen summation inequality are hardly extensible to general ones since there have still not been general discrete orthogonal polynomials applicable to the developments of summation inequalities. Motivated by such observations, this paper proposes novel discrete orthogonal polynomials and then successfully derives general summation inequalities. The resulting summation inequalities are discrete‐time counterparts of the Bessel‐Legendre inequalities but are not based on the discrete Legendre polynomials. By developing hierarchical stability criteria based on the proposed summation inequalities, the effectiveness of the proposed approaches is demonstrated via three numerical examples for the stability analysis of discrete‐time systems with time‐varying delays.     

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems (MJTDSs), whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance, auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function (ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally, numerical examples are given to show the effectiveness and the merits of the proposed method.