LURIE控制系统的时滞相关绝对稳定性判据

1 引言关于具有时滞的Lurie控制系统的绝对稳定性的讨论已有不少结果[1～4],其绝对稳定性条件有时滞无关条件和时滞相关条件两种.由于时滞无关条件缺少了时滞的信息,因此必然会使其稳定性具有保守性.下面对具有多个时变时滞的Lurie控制系统,利用不同于文献[1]的方法进行讨论,给出系统绝对稳定的时滞相关判据.算例表明,与文献[1]的结果相比本文结果可降低保守性.     

具有多状态和控制时滞的控制系统的绝对稳定性分析

基于线性矩阵不等式方法, 对具有多个状态和控制的时变时滞的Lurie型控制系统的稳定性进行分析, 得到了系统绝对稳定的几个充分条件, 这些条件用线性矩阵不等式表示, 具有较低的保守性. 最后通过一个实例验证了所得条件的保守性较以往结果的保守性小.     

具有时滞的Lurie型控制系统绝对稳定的时滞相关准则

研究了具有时滞的Lurie型控制系统的绝对稳定性,利用矩阵不等式的方法出了系统绝对稳定的时滞相关准则,与现有的结果相比,具有较小的保守性。     

多时滞Lurie控制系统的时滞相关鲁棒稳定性

时滞Lurie控制系统的稳定性条件与Lyapunov函数的选取有关.本文对多时滞Lurie控制系统进行了变换,然后选择一个适当的Lyapunov函数,利用Lyapunov稳定性方法并结合Moon引理,得到了多时滞Lurie控制系统的时滞相关鲁棒稳定性判别条件,该条件是以线性矩阵不等式(LMI)给出的,可用Matlab求解.最后用一个算例验证了所得方法的有效性.     

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.     

Lurie滞后反馈控制系统绝对稳定的鲁棒扰动界

本文应用Lyapunov方法讨论了具有时滞反馈的 Lurie控制系统的鲁棒绝对稳定性,给出了具有一个和多个滞后反馈的Lurie控制系统的绝对 鲁棒稳定的充分条件．用本文的结论可直接计算具有时滞反馈的Lurie控制系统绝对稳定的 鲁棒扰动上界．文末给出了应用本文结论的例子．     

多时变状态和控制时滞系统的绝对稳定性

研究了具有多时变状态和控制时滞的Lurie控制系统基于线性矩阵不等式(LMI)的绝对稳定性条件.首先,构造了关于Lyapunov泛函中正定矩阵和积分项系数等自由参数的LMI,获得了系统时滞无关绝对稳定条件.进一步引入自由权矩阵来表示牛顿-莱布尼兹公式中各项的相互关系,得到了系统绝对稳定的时滞相关条件.最后,通过一个实例阐述了本文方法的有效性和相比已有结果的优越性.     

中立型一般Lurie系统绝对稳定的时滞相关准则

研究了具有时滞的中立型一般Lurie系统的绝对稳定性问题.利用Lyapunov方法给 出了系统在无限扇形角内绝对稳定的时滞相关准则,所给的判定条件是线性矩阵不等式(LMI) 形式的,可以很方便地运用Matlab工具箱求解.一个应用的例子表明与现有的一些准则相比, 本文所给的条件具有较小的保守性.     

关于Lurie型控制系统的鲁棒绝对稳定性

用Lyapunov函数法研究了区间Lurie型间接控制系统与直接控制系统的鲁棒绝对 稳定性,给出了系统鲁棒绝对稳定的充分条件.一个应用实例说明该方法的优越性.     

不确定Lurie时滞系统绝对稳定性分析

研究了不确定Lurie时滞系统的绝对稳定问题。通过构造适当的Lyapunov泛函、引入一些自由权矩阵和充分考虑时滞导数的上限信息,得到了基于LMIs(线性矩阵不等式)形式的时滞相关绝对稳定性新准则,两个数值例子验证了所得结论的有效性和更弱保守性。     

Absolute stability of Lurie networked control systems

This paper is concerned with the absolute stability problem of networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. First, in consideration of both the time‐varying network‐induced delays and data packet dropouts, the Lurie NCSs can be modeled as a multiple‐delays Lurie system. Then, a delay‐dependent absolute stability condition is established by using the Lyapunov–Krasovskii method. Next, two approaches to controller design are proposed in the terms of simple algebra criteria, which are easily solved via the toolbox in Matlab. Furthermore, the main results can be extended to robust absolute stability of Lurie NCSs with the structured uncertainties, where robust absolute stability conditions and approaches to robust controller design are presented. Finally, two numerical examples are worked out to illustrate the feasibility and the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.     

Absolute stability and stabilization for Lurie networked control systems

This paper investigates the problem of absolute stability and stabilization for networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. By considering the relationship between the network‐induced delay and its upper bound, an improved stability criterion for networked control system is proposed. Furthermore, the resulting condition is extended to design a state feedback controller by employing an improved cone complementary linearization (ICCL) algorithm. A numerical example is worked out to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

Stability of Networked Control Systems With Uncertain Time-Varying Delays

In this technical note, a new approach for the stability analysis and controller synthesis of networked control systems (NCSs) with uncertain, time-varying, network delays is presented. Based on the Jordan form of the continuous-time plant, a discrete-time representation of the NCS is derived. Using this model for delays that can be both smaller and larger than the sampling interval, sufficient LMI conditions for stability and feedback stabilization are proposed. The results are illustrated by a typical motion control example.      

一类具有离散与分布时滞的控制系统的绝对稳定性

用Lyapunov泛函法研究一类具有离散与分布时滞的控制系统的绝对稳定性问题。给出了这类系统绝对稳定的时滞相关准则。应用实例表明,与现有结果相比,所得结果具有较小的保守性。     

不确定多重时滞随机中立系统鲁棒H∞控制

针对一类不确定多重时滞随机中立系统,研究了鲁棒H_∞控制设计问题．该随机中立系统的状态项、控制项、微分项、外部干扰输入项均含有时滞,系统中的不确定性满足广义匹配条件．首先,利用随机Lyapunov稳定性理论和Ito微分法则,推导出系统的随机鲁棒可镇定的充分条件．在此基础上,进一步给出了鲁棒H_∞控制器存在的充分条件．本文的研究结果以线性矩阵不等式的形式给出,仿真结果表明了此控制器设计方法的有效性．