控制工程 ›› 2013, Vol. 20 ›› Issue (5): 976-979.

• 综述与评论 • 上一篇    下一篇

具LTI 保持的采样控制系统鲁棒稳定性分析

李夏雨金惠良董穗融钟庆昌   

  • 出版日期:2013-09-20 发布日期:2013-11-28

Robustness of Sampled-Data Control Systems with LTI Hold Functions

LI Xia-yuJIN Hui-liangDONG Sui-rongZHONG Qing-chang   

  • Online:2013-09-20 Published:2013-11-28

摘要:

将美国密歇根大学的学者Bernstein 教授和Hollot 教授[1]提出的利用指数矩阵形
式检测鲁棒稳定性的方法,推广到具有线性时不变( LTI) 保持函数的采样控制系统中。直接使
用了连续时间模型的原有数据,避免判断条件过于保守。构造了此类系统的标准Lyapunov 函
数的一个上限。此上限完全不依赖于系统原来的不确定参数,而只依赖于一个为了避免此上
限过于保守而专门引入的一个自由标量参数。给出了一个可靠的数值计算的算法。并且将计
算方法进行改进以进一步适用于具有任意广义采样保持函数( GSHF) 的采样控制系统。

关键词: 鲁棒稳定性, 采样控制, LTI 保持, GSHF, Lyapunov 函数上限

Abstract:

This paper extended Bernstein and Hollot's robust stability test to linear time-invariant ( LTI) uncertain sampled-data control
systems. Unlike that of the most previous works,it directly uses the data of the continuous-time plant and therefore it is expected to be
less conservative. This paper uses exponential-like structure construct an upper bound on the standard quadratic Lyapunov function.
This upper bound is independent of the uncertain parameters but a free scalar parameter which is artificially introduced to reduce the
conservativeness of the upper bound. This paper gives out a reliable numerical algorithm. And then this algorithm is improved so that it
can be used to check the robust stability condition for system with an arbitrary GSHF.

Key words: robust stability, sampled -data control, LTI hold, GSHF, upper bound of Lyapunov function