A generalization of the matrix-sign-function solution for algebraic Riccati equations. (English) Zbl 0598.15012
The matrix sign function is applied to the solution of the generalized algebraic Riccati equation \(A^ T\times E+E^ T\times A-E^ T\times BR^{-1}B^ T\times E+Q=0\) where E is singular or ill-conditioned. The method can also be used for the discrete time generalized algebraic Riccati equation. The algorithm is an iterative method which avoids inverting certain matrices which may be ill-conditioned.
Reviewer: J.A.Ball
MSC:
| 15A24 | Matrix equations and identities |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C55 | Discrete-time control/observation systems |
| 65F30 | Other matrix algorithms (MSC2010) |
References:
| [1] | DOI: 10.1109/PROC.1984.13083 · doi:10.1109/PROC.1984.13083 |
| [2] | DOI: 10.1080/00207178008910040 · Zbl 0464.93029 · doi:10.1080/00207178008910040 |
| [3] | BARRAUD A. Y., R.A.I.R.O. Automatique 13 pp 335– (1979) |
| [4] | DOI: 10.1109/CDC.1984.272049 · doi:10.1109/CDC.1984.272049 |
| [5] | BYERS , R. , 1983 , Hamiltonian and symplectic algorithms for the algebraic Riccati equation . Ph.D. dissertation , Department of Computer Science, Cornell University . |
| [6] | DONGARRA J., UNPACK Users’ Guide (1979) |
| [7] | DOI: 10.1016/0024-3795(83)90104-0 · Zbl 0507.15007 · doi:10.1016/0024-3795(83)90104-0 |
| [8] | LAUB A. J., Proc. 21st I.E.E.E. Conf. on Decision and Control pp 55– (1982) |
| [9] | DOI: 10.1080/00207178008922881 · Zbl 0463.93050 · doi:10.1080/00207178008922881 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
