摘要
目的研究了一类同时具有匹配不确定性和不匹配不确定性的时滞奇异系统鲁棒H∞控制问题。方法构造了Lyapunov泛函,通过适当地放大不等式,利用矩阵Schur补的性质,将问题转化为线性矩阵不等式的求解问题。结果对于所有容许的不确定性,基于矩阵不等式给出了二次稳定的条件并对系统的H∞性能进行了分析和设计;给出了系统的鲁棒H∞控制器,该控制器不仅满足系统二次稳定的条件,而且也满足H∞性能约束。数值算例说明了控制器设计方法的有效性和可行性。结论通过线性矩阵不等式来判断系统是否二次稳定和具有H∞性能并设计其H∞控制律,方法简便,并且比以往结果更有一般性。
Aim To study the robust H∞ control problem of a class of uncertain singular systems with matched and unmatched uncertainties and time-delay. Methods Lyapunov function is constructed and properly enlarging inequality,problems are solved by LMI techniques. Results The condition of quadratic stabilization is given and the H∞ performance of the systems is analyzed and designed for all admissible uncertainties. The robust H∞ controller which satisfies not only quadratic stabilization but also H∞ performance is developed. A numerical example is given to demonstrate the effectiveness and feasibility of the controller.Conclusion Decide whether the system satisfies the condition of quadratic stabilization and the H∞ performance or not by LMI, and design its H∞ controller,which is simple. Moreover, the results provided here generalized the corresponding results in references.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2007年第2期93-96,共4页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
国家自然科学基金资助项目(10571114)
关键词
不确定性奇异系统
二次稳定
时滞
H∞性能
鲁棒控制器
线性矩阵不等式
uncertain singular system
quadratic stabilization
time-delay
H∞ performance
robust controller
linear matrix inequality
