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.     

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.     

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.     

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.     

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.     

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.     

带时滞的线性时变奇异系统的稳定性

通过比较方法建立了一类带时滞的线性时变奇异系统的稳定性判据,并讨论了相应的带有时滞的时变区间奇异系统的稳定性,给出了一个稳定性的比较定理。     

基于推广的概率分布区间分解法的时滞系统稳定性分析

基于推广的概率分布区间分解法,研究一类具有随机时滞系统的概率分布相关稳定性问题.充分利用随机时滞的概率分布信息,获得一系列稳定性判据;通过严格的数学证明,表明通过增加概率区间数可以逐渐降低稳定性判据的保守性,从而建立一组新的分层结构LMI条件;严格证明了在采用相同概率区间划分的条件下,所得到的稳定性判据的保守性低于不考虑时滞概率分布的时变时滞分解法所得到的结果,并且分析和比较了两种方法的计算量.     

直流微电网分布式控制的时滞稳定化设计

直流微电网中,大部分控制器在设计时未考虑通信延时对系统性能的影响,这可能会导致控制器在实际应用中失效甚至影响系统的稳定性.本文基于一种分布式控制策略,建立了直流微电网系统的时滞模型,重点研究了通信延时对系统稳定性的影响.结合Razumikhin稳定性理论,提出了一种针对时变时滞系统的全时滞稳定性判据.为了更加适用于实际系统,在另一种全时滞稳定性判据的基础上,对系统时滞相关稳定性进行分析,得到保证系统稳定的延时上界,进而给出了一种确定控制参数范围的方法.与传统的将通信延时处理为一阶惯性环节的分析方法相比,基于时滞系统的分析方法更切合实际,为系统的稳定运行提供了一个更宽的时滞范围,提高了系统的可靠性.仿真和实验结果表明本文提出的控制参数设计方法能保证系统在最大延时下的稳定运行.     

A stability criterion for singular systems with two additive time-varying delay components

The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities (LMIs). Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.     

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。     

短时延广义网络控制系统的指数保性能控制

本文基于标称点方法,在短时变时延条件下,研究了广义网络控制系统的指数稳定保性能控制问题.基于李雅普诺夫稳定性判据和线性矩阵不等式技术,给出了使得系统能够指数稳定且满足二次型性能指标的状态反馈控制器存在的条件和设计方法.通过采用标称点方法,有效地解决了现有方法没有考虑网络诱导时延与系统保守性的关系且适用范围有限的问题,并通过算例验证了有效性.由于建模过程中充分考虑了系统的保守性,相比之下获得了更好的二次型性能指标值.     

Stability analysis for linear switched systems with time-varying delay.

This correspondence considers the stability problem for a class of linear switched systems with time-varying delay in the sense of Hurwitz convex combination. The bound of derivative of the time-varying delay can be an unknown constant. It is concluded that the stability result for linear switched systems still holds for such systems with time-varying delay under a certain delay bound. Moreover, the delay bound of guaranteeing system stability can be easily obtained based on linear matrix inequalities (LMIs). As a special case, when the time-varying delay becomes constant, the criterion obtained in this correspondence is less conservative than existing ones. The reason for less conservativeness is also explicitly explained in this correspondence. Simulation examples illustrate the effectiveness of the proposed method.     

Stability Analysis for Time-delay Systems via a Novel Negative Condition of the Quadratic Polynomial function

This paper studies the stability analysis problem for time-varying delay systems. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed where its derivative is a quadratic polynomial function of the delay. A novel negative condition of the mentioned quadratic function with two variable parameters is developed to ensure that the LKF derivative is negative, reducing conservatism on some similar results. Besides, an extended version of Bessel-Legendre inequality is introduced to be employed in the stability analysis of time-varying delay systems. Then, some stability criteria with less conservatism are derived for two kinds of the time-varying delay. Finally, the effectiveness of the proposed stability criteria is demonstrated through three examples.

     

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.     

IQC analysis of reset control systems with time-varying delay

The study of input–output stability of reset control systems with time-varying delay is addressed in this work. The time-varying function that defines the delay is assumed to be bounded on magnitude and variation. This approach also covers the particular case of constant time delay, but it is studied separately to obtain less conservative results. After proposing a convenient loop transformation, the stability analysis is performed by means of the integral quadratic constraint framework. Then by applying the Kalman–Yakubovich–Popov lemma, easily checkable conditions in form of linear matrix inequalities are obtained. To conclude, some numerical examples are provided illustrating the proposed criteria.     

Delay-Independent Stability Conditions for Time-Varying Nonlinear Uncertain Systems

A new stability criterion for time-varying systems consisting of linear and norm bounded nonlinear terms with uncertain time-varying delays is formulated. An explicit delay-independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms. The obtained condition turns out to be also necessary if the matrix of the linear part is time-invariant and symmetric; it is shown that these systems satisfy the well-known Aizerman's conjecture. The obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems; in all cases the proposed criterion provides less conservative stability bounds.     

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.