报 告 人：刘建州
报告题目：New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation
报告时间：2017年12月9日（周六）下午15:00—16:00
报告地点：静远楼204学术报告厅
主办单位：数学与统计学院、科技处
报告人简介：
刘建州，博士，教授，博士生导师，一直从事数学的教学与科研。现任中国数学学会常务理事、湖南省运筹学会副理事长、湖南省数学学会常务理事、秘书长，美国《数学评论》评论员，三国际期刊编委，其中一期刊为SCI期刊。主持国家自科基金项目三项和其它省部级项目多项；参加国家自科基金重大研究计划重点支持项目一项。发表论文100余篇，其中SCI、EI收录70余篇，获湖南省自然科学奖三等奖一项(主持)、省级教学成果奖二、三等奖各一项(主持)；湖南省高等学校优秀教材奖一项（主编）。
报告摘要：
The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this talk, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we provider corresponding numerical examples to illustrate the effectiveness of the derived results.
