带时变时滞的不确定离散奇异系统鲁棒稳定性分析  

Analysis of robust stability for uncertain discrete singular systems with time-varying delay

作　　者：翁发禄[1,2] 毛维杰[1] 

机构地区：[1]浙江大学控制科学与工程学系,杭州310027 [2]江西理工大学电气工程与自动化学院,赣州341000

出　　处：《东南大学学报（自然科学版）》2012年第A01期92-97,共6页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61074045;60721062)

摘　　要：为了降低不确定离散奇异时变时滞系统稳定性条件的保守性,首先,采用时滞分割方法,获得了新的时滞系统描述方法,并通过综合考虑各时滞分割子区间,提出了分割子区间依赖型Lyapunov函数.其次,采用时滞依赖线性矩阵不等式技术,将研究结果描述成易于求解的严格线性矩阵不等式形式.通过Matlab工具箱求解线性矩阵不等式,即可获得标称系统正则、因果及均方稳定的条件,并将标称系统的研究结果推广至不确定离散奇异时变时滞系统的稳定性分析,获得了不确定离散奇异时变时滞系统鲁棒稳定判定条件.最后通过实例应用说明了所提定理的有效性,且与现有文献结果相比,保守性得到了较大程度的降低.In order to decrease the conservatism of the stability conditions for uncertain discrete sin gular systems with interval timevarying delay, a delay partitioning technique is employed to obtain a new description of the singular system first, and a new subintervaldependent Lyapunov functional is constructed in comprehensive consideration of all subintervals. Then, based on the delaydependent linear matrix inequality （LMI） method, the obtained result is described into easily solvable strict LM1. By solving the obtained LMI with Matlab toolbox, the condition is obtained for the nominal system to be regular, causal, and meansquare stable. Furthermore, the obtained result is also ex tended to the uncertain case, and the robust stability for the uncertain singular system is guaranteed. Finally, numerical examples are given to show the effectiveness of the proposed theorems. Com pared with the existing results, the theorems in this paper are with much less conservatism.

关 键 词：时滞分割技术 鲁棒稳定 奇异系统 不确定性 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]