### Abstract

In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

Original language | English |
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Pages (from-to) | 933-954 |

Number of pages | 22 |

Journal | Taiwanese Journal of Mathematics |

Volume | 14 |

Issue number | 3 A |

DOIs | |

Publication status | Published - 2010 Jan 1 |

### Fingerprint

### Keywords

- Algebraic riccati equation
- Invariant subspace
- Singular
- Structured doubling algorithm

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Taiwanese Journal of Mathematics*,

*14*(3 A), 933-954. https://doi.org/10.11650/twjm/1500405875

**A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices.** / Chiang, Chun Yueh; Fan, Hung Yuan; Lin, Wen Wei.

Research output: Contribution to journal › Article

*Taiwanese Journal of Mathematics*, vol. 14, no. 3 A, pp. 933-954. https://doi.org/10.11650/twjm/1500405875

}

TY - JOUR

T1 - A structured doubling algorithm for discrete-time algebraic riccati equations with singular control weighting matrices

AU - Chiang, Chun Yueh

AU - Fan, Hung Yuan

AU - Lin, Wen Wei

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

AB - In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal 1/2 when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

KW - Algebraic riccati equation

KW - Invariant subspace

KW - Singular

KW - Structured doubling algorithm

UR - http://www.scopus.com/inward/record.url?scp=77954160235&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954160235&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500405875

DO - 10.11650/twjm/1500405875

M3 - Article

AN - SCOPUS:77954160235

VL - 14

SP - 933

EP - 954

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 3 A

ER -