时滞系统时滞相关型稳定性准则

针对常数时滞线性系统的稳定性问题,基于一个适当形式的Lyapunov-Krasovskii泛函,通过利用一个积分不等式,采用时滞分解方法,以线性矩阵不等式的形式给出了时滞系统的时滞相关型稳定性准则.与现有的时滞相关型稳定性结果相比较,所得到的结果具有保守性更好,结构更加简单,且不合有任何多余的矩阵变量等特点,并从理论上进行了严格的证明,解决了现有的稳定性结果绝大多数只是从数值例子说明其有效性的问题.示例说明了所得结果的有效性.     

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.     

离散时滞切换系统稳定性分析

对于一类子系统为离散时滞系统的切换系统,研究渐近稳定性条件和切换信号的选取方法．根据李亚普诺夫稳定性理论，推出以线性矩阵不等式表示的在任意切换信号作用下系统渐近稳定的两个充分性条件，在此基础上进一步给出了系统渐近稳定的凸组合条件和切换信号的选取方法．仿真实例验证了所设计的切换方案的有效性．     

混合变时滞不确定中立型系统鲁棒稳定性分析

研究一类含混合变时滞不确定中立系统时滞相关鲁棒稳定性问题。基于时滞中点值,把时滞区间均分成两部分,通过构造包含时滞中点信息的增广泛函和三重积分项的Lyapunov-Krasovskii (L-K)泛函,利用L-K稳定性定理、积分不等式方法和自由权矩阵技术,建立了一种基于线性矩阵不等式(LMI)的、与离散时滞和中立时滞均相关的鲁棒稳定性判据。数值算例表明,该判据改善了已有文献的结论,具有更低的保守性。     

线性时滞系统稳定性分析综述

时滞在工程领域广泛存在,对此综述了线性时滞系统的稳定性研究方法.从频域和时域两个角度详细介绍了各种方法的特点,着重讨论基于线性矩阵不等式(LMI)的分析方法,指出保守性是分析的重点.对现有结果的保守性进行比较和评述,并提出了改进的思路.     

离散广义时滞系统的时滞依赖稳定性分析

讨论离散广义时滞系统的稳定性问题. 在不使用系统分解和等价转换的情况下, 利用线性矩阵不等式方法, 给出保证系统正则、因果和稳定的时滞依赖条件. 与已有的方法相比, 本文的方法更加充分地利用时滞的信息, 因此所得结果具有较小的保守性. 数值例子说明本文结果的有效性.     

混合时滞不确定中立系统鲁棒稳定的时滞分割方法

研究了一类同时具有离散与分布时滞的不确定中市型系统的鲁棒稳定性问题.基于时滞分割思想,通过构造一类特殊的Lyapunov-Krasovskii泛函,并利用Jensen不等式,建立了线性矩阵不等式形式的时滞相关鲁棒稳定性新判据.该方法不涉及模型变换与自由权矩阵技术,减少了理论与计算上的复杂性;同时允许中立时滞项的系数矩阵...     

基于LMI方法的时滞细胞神经网络稳定性分析

神经网络是一个复杂的大规模非线性系统,而时滞神经网络的动态行为更为丰富和复杂．现有的研究时滞神经网络稳定性的方法中最为流行的是Lyapunov方法．它把稳定性问题变为某些适当地定义在系统轨迹上的泛函,通过这些泛函相应的稳定性条件就可以获得．该文得到了时滞细胞神经网络渐近稳定性的一些充分条件．作者利用了泛函微分方程的Lyapunov—Krasovskii稳定性理论和线性矩阵不等式(LMI)方法,精炼和推广了一些已有的结果．它们比目前文献报道的结果更少保守．该文还给出了确定时滞细胞神经网络稳定性更多的判定准则．     

具有时变输入时滞的不确定T-S模糊系统的鲁棒稳定性

本文主要针对不确定的输入变时滞 T-S 模糊系统设计模糊控制器使系统鲁棒稳定. 首先基于 Lyapunov-Krasovskii 泛函方法, 通过引入更多的松弛变量矩阵, 以 LMI 形式给出使此模糊系统稳定的充分条件. 在设计模糊控制器时并不要求满足时变输入时滞的导数小于1的限制条件. 最后给出数值仿真例证本文提出的结果的有效性且保守性更小.     

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.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.     

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also eiven.     

时滞切换系统的时滞相关性稳定判据

考虑由时滞子系统构成的切换系统,分析其在任意切换作用下保持指数稳定性的条件．利用较为一般的Lyapunov—Krasovskii泛函构造方式及相关的解析技巧给出了以线性矩阵不等式表述的时滞相关性稳定判据;进而证明了其指数衰减率对于所有切换序列一致成立,即其完全取决于子系统的结构特征．仿真算例证实了方法的有效性．     

含状态和输入时滞的网络控制系统镇定

研究含有更广泛被控对象的网络控制系统镇定问题．假定被控对象含有时变状态和输入时滞,采用Lyapunov-Krasovskii泛函方法分析了系统的稳定性．所提出的方法可转化为线性矩阵不等式的形式,因而可较为容易地求得控制器和广义最大允许时延．仿真结果说明了所提出方法的有效性．     

Stability of PID-controlled second-order time-delay feedback systems

In the previous papers, the stability of PID-controlled first-order time-delay systems has been investigated by means of several methods, of which the Nyquist criterion, a generalization of the Hermite–Biehler Theorem, and the root location method are well known. Explicit expressions of the boundaries of the stability region, which is the set of controller parameters that give stable closed-loop systems, have been determined. From these studies, one can verify that not all plants can be made stable and then obtain the set of process parameters that allow stable closed-loop systems. With this set, one can implement the stability region of the process parameters. In a recent paper the stability conditions based on Pontryagin’s studies and valid for arbitrary-order plants have been presented. The procedure deduced for the controller parameters is exhaustive, but that deduced for the process parameters requires further mathematical evaluations, whose complexity is proportional to the number of process time constants. In the aforementioned recent paper these evaluations have been performed for a second-order time-delay plant whose transfer function has no zero. The aim of this paper is to execute these calculations for a second-order plant whose transfer function has one zero and to provide the related stability region.     

Stability analysis of systems with time-varying delay via relaxed integral inequalities

This paper investigates the stability of linear systems with a time-varying delay. The key problem concerned is how to effectively estimate single integral term with time-varying delay information appearing in the derivative of Lyapunov–Krasovskii functional. Two novel integral inequalities are developed in this paper for this estimation task. Compared with the frequently used inequalities based on the combination of Wirtinger-based inequality (or Auxiliary function-based inequality) and reciprocally convex lemma, the proposed ones can provide smaller bounding gap without requiring any extra slack matrix. Four stability criteria are established by applying those inequalities. Based on three numerical examples, the advantages of the proposed inequalities are illustrated through the comparison of maximal admissible delay bounds provided by different criteria.     

Wirtinger-based integral inequality: Application to time-delay systems

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.     

Stability analysis of time-delay systems via free-matrix-based double integral inequality

Based on the free-weighting matrix and integral-inequality methods, a free-matrix-based double integral inequality is proposed in this paper, which includes the Wirtinger-based double integral inequality as a special case. By introducing some free matrices into the inequality, more freedom can be provided in bounding the quadratic double integral. The connection of the new integral inequality and Wirtinger-based double one is well described, which gives a sufficient condition for the application of the new inequality to be less conservative. Furthermore, to investigate the effectiveness of the proposed inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. Numerical examples are given to demonstrate the advantages of the proposed method.     

On input-to-state stability of systems with time-delay: A matrix inequalities approach

Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L₂-gain analysis, is extended to input-to-state stability (ISS). We first obtain sufficient conditions for ISS of systems with time-varying delays via Lyapunov-Krasovskii method. NLMIs are derived then for a class of systems with delayed state-feedback by using the S-procedure. If NLMIs are feasible for all x, then the results are global. When NLMIs are feasible in a compact set containing the origin, bounds on the initial state and on the disturbance are given, which lead to bounded solutions. The numerical examples of sampled-data quantized stabilization illustrate the efficiency of the method.