东北大学学报（自然科学版）

东北大学学报（自然科学版） ›› 2013, Vol. 34 ›› Issue (12): 1691-1694.DOI: 10.12068/j.issn.1005-3026.2013.12.005

• 信息与控制 • 上一篇    下一篇

不确定线性离散时滞系统的指数稳定性

郑连伟1，宋叔尼1，戴良萃2   

  1. (1.东北大学理学院，辽宁沈阳110819；2.红塔辽宁烟草有限公司，辽宁沈阳110001)
  • 发布日期:2013-07-09
  • 通讯作者: 郑连伟
  • 作者简介:郑连伟(1963-)，男，辽宁新民人，东北大学副教授，博士；宋叔尼(1962-)，男，湖南澧县人，东北大学教授.
  • 基金资助:
    辽宁省自然科学基金资助项目(201102070).

Exponential Stability for Uncertain Linear DiscreteTime Systems with TimeVarying Delays

ZHENG Lianwei1， SONG Shuni1， DAI Liangcui2   

  1. 1. School of Sciences， Northeastern University， Shenyang 110819， China; 2. Hongta Liaoning Tobacco Corporation， Shenyang 110001， China.
  • Published:2013-07-09
  • Contact: ZHENG Lianwei
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摘要： 采用属于超长方体的时变参数向量描述不确定性，利用仿射依赖于参数的Lyapunov泛函研究不确定线性离散时滞系统的指数稳定性问题，由Lyapunov泛函的指数衰减性保证系统的指数稳定性.引入仿射依赖于参数的自由权矩阵分析Lyapunov泛函的指数衰减性，利用多凸函数的性质把含时变参数的矩阵不等式转化成线性矩阵不等式，从而得到了指数稳定的充分条件.由于有效利用了不确定时变参数和其增量的上下界信息，并且采用凸组合方法处理区间时变时滞，因此所得方法具有较小的保守性.最后用数值算例验证了所得方法的有效性.

关键词: 时变时滞, 离散系统, 指数稳定性, 不确定参数, 线性矩阵不等式

Abstract: The uncertainties were described as timevarying parameter vectors belonging to a hyper rectangle. The problem of exponential stability for uncertain linear discretetime systems with timevarying delays was investigated by using affine parameterdependent Lyapunov functional. Exponential stability was guaranteed by the exponential decay of the Lyapunov functional. Affine parameterdependent freeweighting matrices were introduced to analyze the exponential decay of the Lyapunov functional， and the matrix inequalities containing timevarying parameters were transferred to linear matrix inequalities by using the properties of multiconvex function. Therefore， a sufficient condition for exponential stability was obtained. Since the information of upper and lower bounds of the uncertain timevarying parameters and their increments was effectively used and the convex combination method was applied when handling interval timevarying delay， the proposed method had less conservatism. An example was presented to show the effectiveness of the proposed method.

Key words: timevarying delay, discretetime system, exponential stability, uncertain parameters, linear matrix inequalities

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