A parametrization of solutions of the discrete-time algebraic Riccati equation based on pairs of opposite unmixed solutions

被引：11
|
作者：
Wimmer, HK [1 ]
机构：
[1] Univ Wurzburg, Math Inst, D-97074 Wurzburg, Germany
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2006年 / 44卷 / 06期
关键词：
discrete-time algebraic Riccati equation; unmixed solutions; opposite solutions; parametrization by invariant subspaces; shorted operators; Schur complements;
D O I：
10.1137/S0363012904441362
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The paper describes the set of solutions of the discrete-time algebraic Riccati equation. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution. The results of the paper provide an extended counterpart of the parametrization theory of continuous-time algebraic Riccati equations by Willems, Coppel, and Shayman.
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页码：1992 / 2005
页数：14
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