不确定离散系统的最优保性能控制_俞立.pdf

第 16 卷第 5 期 控制理论与应用 Vol . 16 ,N o . 5 　1999 年 10 月 CON TROL THEOR Y AND APPL ICA TIONS Oct . , 1999 　 不确定离散系统的最优保性能控制 俞 　立 ( 浙江工业大学信息工程学院 ·杭州 ,310032) 　　摘要 : 对一类具有范数有界时变参数不确定性的离散时间线性系统和一个二次型性能指标 , 研究其最优保性 能状态反馈控制律的设计问题. 通过采用线性矩阵不等式方法 , 导出了存在保性能控制律的一个充分必要条件 , 进 而 ,证明了该条件等价于一个线性矩阵不等式的可解性问题 , 并用这组线性矩阵不等式的可行解给出了保性能控 制律的一个参数化表示. 在此基础上 ,通过建立并求解一个凸优化问题 ,给出了最优保性能控制律的设计方法. 　　关键词 : 离散系统; 不确定性; 保性能控制; 线性矩阵不等式 Op t i m al Gu a r a n t e e d Cost Con t r ol f or U n c e r t ai n Disc r e t eTi m e L i n e a r Syst e m s Yu Li ( College of Information Engineering , Zhej iang University of Technology ·Hangzhou ,310032 , P . R . China) 　　A b st r a ct : For a class of discretetime linear systems with normbounded timevarying p arameter uncertainty and a quadratic cost index , the problem of designing an optimal guaranteed cost state feedback controller is considered in this p ap er . A necessary and sufficient condition for the existence of guaranteed cost controllers is derived . Furthermore , it is shown that this condition is equivalent to the solvability problem of a system of linear matrix inequalities , and its solutions provide a p arametrized representation of guaranteed cost controllers . Based on that , the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem , which can be solved by the existing convex optimization techniques . Finally , an example is given to illustrate the prop osed results . 　　Key w or ds : discretetime system