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.     

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。     

中立型线性时滞系统的时滞相关稳定性

讨论中立型线性时滞系统的时滞相关稳定性.首先将中立型系统转化为广义系统,然 后利用Lyapunov-Krasovskii V泛函方法,在处理V的导数时,不进行放大估计,而通过引入一 些恰当的0项,构造多个LMI,从而获得基于多个LMI的时滞相关稳定充分条件.最后的数值 例子说明所得的结论较已有文献具有较小的保守性.     

具有区间时变时滞2-D 离散系统的时滞相关稳定与控制

针对具有区间时变时滞2-D离散系统,利用时滞相关方法,研究其稳定性与控制问题.首先选取含有时滞项上、下界的一个新的Lyapunov函数,对其差分时考虑所有项,得到了基于线性矩阵不等式(LMI)的时滞相关稳定性准则;然后给定时变时滞项的下界,再由一个凸优化问题最大化其上界,进而通过状态反馈实现系统的时滞相关控制,且求解LMI可得到增益矩阵;最后,利用数值算例说明了所得结果有效且优于已有成果.     

经过一种PTVD补偿的带有快变中立型时滞的系统的时滞依赖稳定性

研究了一类带有时变时滞的线性中立型系统的稳定性, 其中中立型项中的时滞包括一类快变时滞(即, 时滞导数大于1). 目前, 还没有文献考虑带有这种带有快变中立型时滞的系统. 通过使用新的Lyapunov-Krasovskii泛函和带有时滞的多项式(PTVD)补偿技术, 对于此类系统提出了具有更少保守性的时滞依赖稳定性判据. 通过使用新的泛函可以实现处理快变时滞的目的. 同时, 通过使用PTVD补偿技术, 可以在判据中引入一些有用的元素. 而在之前的结果中, 当估计Lyapunov-Krasovskii泛函的上界时, 这些元素通常是被忽略的. 一个数值例子将被提供来验证所得到结果的有效性.     

时变时滞Lurie控制系统的绝对稳定性

基于Lyapunov稳定性定理,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了具有多个时变时滞的Lurie直接控制系统和Lurie间接控制系统的绝对稳定性.所得结论是时滞无关的,即绝对稳定性充分条件仅依赖于时滞导数的大小,特别地,时滞可为无界函数.通过一个示例说明有时得到时滞相关的绝对稳定性条件比时滞无关的稳定性条件具有更大的保守性,促使今后寻找另外的方法和工具得到保守性较低的稳定性条件.仿真示例同时说明此方法对时滞为无界函数时的有效性.     

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.     

具有多个时变时滞的不确定系统的时滞相关稳定性

研究了具有多个时变时滞的不确定系统的 稳定性问题, 利用Razumikhn定理与向量不等式的方法, 给出了不确定时滞系统稳定的充分 条件. 所得的条件与时滞相关, 在很大程度上降低了现有结果的保守性. 文末给出了一个应 用的算例, 并与已有的结果作了比较.     

带马尔科夫跳的模态相关时变时滞随机系统的状态反馈控制器设计

针对带马尔科夫跳的模态相关时变时滞系统得到了一个改进的均方指数稳定结果并设计了状态反馈控制器. 首先, 通过构造一个改进的Lyapunov-Krasovskii泛函, 以线性矩阵不等式的形式给出一个均方指数稳定性条件; 这里, 衰减率可以是一个在区间内取值的有限常数, 同时, 时变时滞的导数上界不要求小于1; 基于得到的稳定性条件, 设计了状态反馈的控制器. 最后, 通过两个仿真算例验证了所得理论的结果的有效性, 并与已有结果相比较, 保守性较弱.     

New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay

This paper focuses on the stability problem for uncertain T-S fuzzy systems with interval time-varying delay. The system uncertainties are assumed to be time-varying and norm-bounded. The time-varying delay is considered as either being differentiable uniformly bounded with delay-derivative bounded by constant interval, or being fast-varying case with no restrictions on the delay derivative. Since we employ a novel Lyapunov-Krasovskii functional (LKF) which contains the information on the time-varying delay, and estimate the upper bound of its derivative less conservatively and adopt the convex optimization approach, some less conservative delay-derivative-dependent stability conditions are obtained in terms of linear matrix inequalities (LMIs), without using any free weighting matrix. These conditions are derived that depends on both the upper and lower bounds of the delay derivatives. Finally, some numerical examples are given to demonstrate the effectiveness and reduced conservatism of the proposed method.     

时变时滞Lurie非线性系统绝对稳定新判据

针对时变时滞Lurie非线性系统,应用增广Lyapunov-Krasovskii泛函结合自由权矩阵方法,研究其时滞相关绝对稳定性问题.通过保留Lyapunov-Krasovskii泛函导数中常被忽略的有用信息,充分考虑时变时滞、时滞上界及它们的差三者之间的关系,得到了具有更低保守性的基于线性矩阵不等式的时滞相关绝对稳定条件.数值实例表明,该方法得出的结果优于已有文献的结果.     

Stability analysis of linear systems with an interval time-varying delay – A delay-range-partition approach

In this paper, the stability analysis problem of linear systems with an interval time-varying delay is investigated. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, which includes more information of the delay’s range and the delay’s derivative. Secondly, based on two improved integral inequalities which are less conservative than Jensen’s integral inequalities, a delay-range-partition (DRP) approach is proposed to estimate the upper bound of the derivative of the augmented Lyapunov-Krasovskii functional. Then, less conservative stability criteria in the form of linear matrix inequality (LMI) are established no matter whether the lower bound of delay is zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numerical examples are given, and their results are compared with the existing results.     

Improved delay‐dependent absolute stability and robust stability for a class of nonlinear systems with a time‐varying delay

This paper investigates the problem of the absolute stability of Lur'e systems with a time‐varying delay. By considering the relationships among the time‐varying delay, its upper bound, and the difference between them, less conservative delay‐dependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov–Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Improved delay-derivative-dependent stability criteria for linear systems using new bounding techniques

In this letter, the problem of delay-derivative-dependent stability analysis for linear systems with interval delay is investigated. By constructing variable delay-decomposition Lyapunov-Krasovskii (LK) functional, some delay-derivative-dependent stability criteria are derived by incorporating with different bounding techniques to estimate some integral terms in the derivative of the LK functional. These criteria are efficient when the upper bound of delay derivative is larger than one. These criteria improve the existing ones with smaller computation burden and less conservatism, which are shown through numerical examples.

     

An extended frequency-domain stability criterion for a class of sampled-data systems

A new frequency-domain stability criterion employing a Popov-type multiplier is obtained for a class of nonlinear sampled-data control systems containing a monotonically nondecreasing nonlinearity. This criterion is an extension of previous results, in that unlike other criteria of this type, no upper bound is placed on the derivative of the nonlinearity. An example is given in which this new criterion is used to obtain stability conditions for a non-linear sampled-data system. These conditions are less restrictive than those obtained using other stability criteria.     

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.     

Dwell time-based stabilisation of switched delay systems using free-weighting matrices

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov–Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.     

On delay-derivative-dependent stability of systems with fast-varying delays

Stability of linear systems with uncertain bounded time-varying delays is studied under the assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound of the L₂-norm of a certain integral operator. There exists a bound on this operator norm in two cases: in the case where the delay derivative is not greater than 1 and in the case without any constraints on the delay derivative. In the present note we fill the gap between the two cases by deriving a tight operator bound which is an increasing and continuous function of the delay derivative upper bound d?1. For d→∞ the new bound corresponds to the second case and improves the existing bound. As a result, for the first time, delay-derivative-dependent frequency domain and time domain stability criteria are derived for systems with the delay derivative greater than 1.