一类耦合代数Riccati方程的解  

The Solution of a Class of Coupled Algebraic Riccati Equations

作　　者：张宇 关晋瑞 宋儒瑛[1] ZHANG Yu;GUAN Jin-rui;SONG Ru-ying(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《宜春学院学报》2024年第3期9-12,共4页Journal of Yichun University

基　　金：国家自然科学基金项目(编号:12001395);山西省科技创新人才团队专项资助(编号:202204051002018)。

摘　　要：耦合代数Riccati方程在控制论中具有广泛的应用,文章研究了一类耦合代数Riccati方程的解。基于M-矩阵和非负矩阵的理论,在一定假设条件下,证明了这类耦合代数Riccati方程存在最小非负解。最后通过数值算例,验证了所得结果的有效性。The coupled algebraic Riccati equations have extensive applications in control theory.In this paper,the solution of a class of coupled algebraic Riccati equations is studied.Based on the theory of M-matrix and non-negative matrix,it is proved that the minimal non-negative solution exists for this kind of coupled algebraic Riccati equation under certain assumptions.Finally,numerical examples are given to verify the validity of the results.

关 键 词：耦合代数Riccati方程 最小非负解 不动点迭代法 

分 类 号：O241.6[理学—计算数学]