基于凸多面体方法的时滞和连续系统稳定性分析  

Stability analysis of systems with two additive time-varying delay components via convex polyhedron method

作　　者：吴海霞[1,2] 冯伟[1,2] 邹晓兵[2] 

机构地区：[1]重庆大学自动化学院,重庆400044 [2]重庆第二师范学院数学与信息工程系,重庆400065

出　　处：《计算机应用研究》2014年第5期1378-1380,共3页Application Research of Computers

基　　金：国家自然科学基金资助项目(61170249;61103211);重庆市青年骨干教师资助计划(2011);重庆市博士后基金资助项目(XM201310)

摘　　要：针对一类状态向量中含有时滞和的连续系统,研究其时滞相关稳定性问题。利用凸组合方法和积分不等式并构造合适的李雅普诺夫泛函,以线性矩阵不等式形式给出了保证系统稳定的时滞相关充分条件,该线性矩阵不等式形式的系统稳定条件易于验证。由于在对李雅普诺夫泛函求导过程中使用了凸多面体方法,使得所得到的结论具有更小的保守性,仿真算例验证了结论的有效性。This paper was concerned with stability analysis for systems. The systems were based on a new time-delay model proposed recently,which contained two successive delay components in the state. By using a convex polyhedron method, em- ploying some integral inequality approach and constructing a new Lyapunov functional, some less conservative stability criteria were established in terms of linear matrix inequalities （LMIs）. Due to the convex polyhedron method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. Numeri- cal example shows that the proposed criterion is effective and an improvement over some existing results in the literature.

关 键 词：连续系统 稳定性 时滞 李雅普诺夫泛函 凸多面体方法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]