具有分布时滞和区间参数的随机系统的p-阶矩指数鲁棒稳定性

研究了一类具有分布时滞和区间参数的随机系统的p-阶矩指数鲁棒稳定性问题,利用Liapunov-Krasovskii泛函、区间矩阵的分解技术及Ito公式,得到了该系统p-阶矩指数鲁棒稳定的时滞依赖的稳定性判据.通过数值例子说明了所得判据的有效性和实用性.     

非线性齐次时滞系统H_∞控制

讨论了非线性齐次时滞系统的H∞控制问题.首先给出了非线性仿射齐次时滞系统的Lyapunov泛函V(x)具体形式,选取适当的λ* ,使得当λ>λ*时系统的Hamilton-Jacobi-Isaacs不等式有解,从而解决了系统的L2 增益问题.文章最后构造了具体状态反馈控制律u(x) ,使时滞Lyapunov泛函V(x)沿闭环系统轨线导数小于零,保证了系统的渐进稳定性,因而解决了系统的H∞控制问题.     

随机时滞混杂区间系统的鲁棒稳定性

利用Lyapunov泛函方法及线性矩阵不等式，得到了随机时滞混杂区间系统的能失性及鲁棒稳定性的充分判据。     

具有混合时滞的区间神经网络的全局指数稳定性

本文研究了一类具有混合时滞的区间神经网络系统的全局指数稳定性.通过选择适当的Lyapunov泛函,运用不等式技巧,得到了用线性矩阵不等式表示的有关的区间神经网络全局指数稳定的充分判据.通过一个数值实例验证了判据的有效性.     

灰色中立线性时滞系统的鲁棒稳定性

首先提出了灰色中立线性时滞系统及其鲁棒渐近稳定性的概念;然后,利用区间灰矩阵的分解技术和矩阵范数不等式及IJyapunov泛函,研究了灰色中立线性时滞系统的鲁棒渐近稳定性,得到了鲁棒渐近稳定的几个充分条件;最后通过数值例子说明了所得结果在实际应用中的方便性和有效性.     

含分布时滞的不确定中立系统鲁棒稳定之时滞分解法

研究了一类同时具有离散与分布时滞的不确定中立型系统的鲁棒稳定性问题,基于时滞分割方法建立一种新的时滞相关鲁棒稳定性条件.通过把时滞区间非均匀的分解成N份,针对不同的分割区间构造合适的Lyapunov-Krasovskii(L-K)泛函,结合积分不等式处理方法建立了基于线性矩阵不等式(LMI)形式的时滞相关条件,该方法不包含任何的模型变换和自由权矩阵技术,减少了理论与计算上的复杂性,最后的数值算例仿真表明,该方法扩大了系统稳定的时滞上界范围,相比已有结论具有更低的保守性.     

一类含变时滞和分布时滞的系统的指数稳定性

基于泛函微分方程的稳定性理论,本文通过构造Lyapunov泛函,在Banach空间中,对一类含变时滞和分布时滞的系统的指数稳定性问题作探讨.     

一类区间随机分布时滞系统的p-阶矩指数稳定性

研究了一类区间随机分布时滞系统的p-阶矩指数稳定性问题.利用分布时滞转化为点时滞方法和区间矩阵的分解技术,得到了该系统p-阶矩指数稳定的时滞依赖的稳定性判据.通过数值例子说明了所得判据的有效性和实用性.     

离散时间二型模糊双线性时滞系统的可达集估计与耗散性

文章研究了一类带有时变时滞和外部干扰的非线性系统的可达集估计与耗散控制问题.首先,考虑非线性系统的不确定参数,将非线性系统建模为区间二型模糊双线性时滞系统.其次,通过构造Lyapunov-Krasovskii泛函,提出区间二型模糊状态反馈控制准则,并利用反互凸组合引理界定二、三重时滞差分交叉项,得到保守性较小的区间二型模糊双线性闭环系统的可达集估计条件及系统严格耗散稳定性充分性条件.定理的条件可以保证系统的所有状态都收敛在一个椭圆内,并通过序列线性规划矩阵方法得到模糊控制器.最后,给出数值算例和仿真结果验证所得结论的有效性和正确性.     

改进的时变时滞Lurie系统绝对稳定性判据与分析

研究一类时变时滞Lurie系统的鲁棒性和绝对稳定性问题.根据时变时滞分段分析方法,引入三重积分算子设计一个新的Lyapunov-Krasovskii泛函,得到一些保守性更小的时滞相关稳定性判据.采用相互凸松弛方法与边界不等式相结合,避免忽略泛函微分中的有用项,减少额外自由变量及计算量.通过数值实验分析表明了所提方法的有效性和先进性.     

LMI approach to exponential stability of linear systems with interval time-varying delays

This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov–Krasovskii functional combined with the Newton–Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.     

Stability analysis for networked control systems with sampling,transmission protocols and input delays

In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems affected by delays and permit multiple jumps at a jumping instant. The stability analysis depends on the Lyapunov–Krasovskii functional approaches for hybrid systems with memory and the proposed stability theorem does not need strict decrease of the Lyapunov–Krasovskii functional during jumps. Based on the developed stability theorems, stability conditions for networked control systems are established. An explicit formula is given to compute the maximal allowable transmission interval. In the special case that the networked control system contains linear dynamics, an explicit Lyapunov functional is constructed and stability conditions in terms of linear matrix inequalities (LMI) are proposed. Finally, an example of a chemical batch reactor is given to illustrate the effectiveness of the proposed results.     

Existence of a global liapunov functional for certain classes of nonlinear distributed systems : PMM vol. 40, n 6, 1976, pp. 1135–1142

The existence of a global Liapunov functional for nonlinear evolutionary equations in a Hilbert space is investigated as a continuation of paper [1], The results obtained represent a generalization of the results of the theory of absolute stability [2, 3], for the systems with infinite dimensional phase space, and are used for investigation of the nonlocal stability and instability of nonlinear distributed systems. The conditions of existence of the global Liapunov functional obtained are illustrated by an example of a nonlinear parabolic system defined in the interval [0, 1], The concept of a Liapunov functional was first introduced and used with success in [4].     

Delay-dependent stability criterion for a class of non-linear singular Markovian jump systems with mode-dependent interval time-varying delays

This paper deals with the problem of stability analysis of non-linear singular systems with Markovian jumping parameters and mode-dependent interval time varying delays. New delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs) by constructing a mode-dependent Lyapunov–Krasovskii functional and using some integral inequalities. Numerical examples are presented to illustrate the usefulness and less conservativeness of the proposed theoretical results.     

Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

In this paper, we aim to investigate the exponential stability of general hybrid stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient to be applied than those Razumikhin‐type conditions in the literature. Meanwhile, we show that unstable hybrid stochastic delay differential systems, both linear and nonlinear, can be stabilized by suitably impulsive sequence. Finally, two examples are discussed to illustrate the effectiveness and advantages of the obtained results. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations

This paper considers the robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. A Lyapunov-Krasovskii functional, which takes the range information of the time-varying delay into account, is proposed to analyze the stability. A new approach is introduced for estimating the upper bound on the time derivative of the Lyapunov-Krasovskii functional. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness of the proposed approach.     

基于积分二次约束混合摄动系统的摄动界

讨论正向通道为线性不确定系统,反馈通道为非线性动态不确定系统组成的不确定混合摄动系统的摄动界问题。假定其线性部分的参数不确定由区间摄动模式描述,非线性部分的动态不确定由积分二次约束(IQC)描述。用Minkowski泛函出给出区间摄动模式下的摄动界的定义,并给出参数空间中混合摄动模式下系统摄动界的估计式。根据双凸函数和凹凸函数的特性把混合摄动系统的无穷稳定检验问题转化为顶点检验和一维检验问题。最后给出例子。     

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays

This paper considers the problem of leader-following consensus stability and also stabilization for multi-agent systems with interval time-varying delays. The randomly occurring interconnection information of the leader and the Markovian switching interconnection information of the agent are matters of concern in the systems. Through construction of a suitable Lyapunov–Krasovskii functional and utilization of the reciprocally convex approach, new delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.