离散广义系统具有完整性的鲁棒二次稳定  

Robust quadratic stabilization with integrity for discrete-time descriptor system

作　　者：陈跃鹏[1] 周祖德[2] 刘焕彬[2] 张庆灵[3] 姚波[4] 

机构地区：[1]武汉理工大学自动化学院 [2]黄冈师范学院数学系,湖北黄冈438000 [3]武汉理工大学机电学院,湖北武汉430070 [4]沈阳师范大学数学与系统科学学院,辽宁沈阳110006

出　　处：《控制理论与应用》2006年第1期14-18,59,共6页Control Theory & Applications

基　　金：国家自然科学基金重点资助项目(50335020);国家自然科学基金资助项目(60574011);中国博士后基金资助项目(2005038553);湖北省教育厅科学研究重大项目基金资助项目(2002z04001)

摘　　要：研究时不变不确定离散广义系统具有完整性的鲁棒二次稳定问题.首先,给出不确定离散广义系统鲁棒二次稳定的充要条件.其次,利用广义代数R iccati不等式,设计状态反馈使得不确定离散广义系统鲁棒二次稳定.进一步,给出状态反馈设计方法,使得不确定离散闭环广义系统在执行器正常以及部分出现故障情况下,都保持鲁棒二次稳定.即不确定广义系统具有完整性.同时,还讨论了所给的广义代数R iccati不等式的求解问题.最后给出数字例子来验证所给结果的有效性.In this paper, robust quadratic stabilization with integrity is explored for an uncertain time-invariant discrete-time descriptor system. Firstly, a sufficient and necessary condition for an uncertain discrete-time descriptor system to be robust quadratically stable is given. Then, in terms of generalized algebraic Riccati inequality, the state feedback is designed such that the resultant uncertain discrete-time closed-loop descriptor system is robustly quadratically stable. Furthermore, attention is focused on the design of state feedback which guarantees the resultant uncertain discretetime closed-loop descriptor system to be robustly qUadratically stable even when part of the actuators failure, i.e. the controlled descriptor system possesses integrity. Simultaneous, the problem of how to solve the generalized algebraic Riccati inequality is also discussed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

关 键 词：完整性 二次稳定 不确定离散广义系统 执行器 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]