具有变时滞中立型控制系统的鲁棒稳定性分析  

Robust stability analysis for uncertain neutral control systems with time-varying delays

作　　者：张海涛[1,2] 王婷[1] 费树岷[1] 李涛[3] 

机构地区：[1]东南大学复杂工程系统测量与控制教育部重点实验室,江苏南京210096 [2]解放军理工大学工程兵工程学院,江苏南京210007 [3]南京航空航天大学自动化工程学院,江苏南京210016

出　　处：《解放军理工大学学报（自然科学版）》2012年第1期12-16,共5页Journal of PLA University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60904023;61004032)

摘　　要：为了更好地解决时滞中立型控制系统的鲁棒稳定性分析问题,研究并建立保守性更小的相关稳定性准则,针对变时滞不确定中立性系统数学模型,通过构造一个新颖的Lyapunov-Krasovskii泛函,将广义凸集合与积分不等式等方法相结合来估计Lyapunov-Krasovskii泛函导函数的上界,有效地拓宽了结论适用范围。在考虑变时滞与其导函数上下界可测同的同时,基于线性矩阵不等式给出了系统渐近稳定与鲁棒稳定的相关准则,这些准则易于借助Matlab工具箱LMI进行求解。最后通过数值算例与现有相关结论进行了对比分析,所得结果具有更大时滞容许上界值,表明所提出的方法在稳定性分析中更具有较低保守性。To better handle the problem on robust stability for neutral control systems, in which time-varying delay was involved, a stability criterion with less conservatism was put forward. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the uncertain neutral control system model. The generalized convex combination and integral inequality techniques were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a cri- terion on asymptotical and robust stability were presented in terms of linear matrix inequality （LMI）, which can be easily checked by resorting to LMI in Matlab Toolbox. Finally, through one numerical example the criterion was compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

关 键 词：中立型控制系统 时滞相关 鲁棒稳定性 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]