### Abstract

Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

Original language | English (US) |
---|---|

Pages (from-to) | 313-326 |

Number of pages | 14 |

Journal | Linear and Multilinear Algebra |

Volume | 46 |

Issue number | 4 |

State | Published - 1999 |

### Fingerprint

### Keywords

- Optimal control
- Riccati equations
- Time-varying systems

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*46*(4), 313-326.

**On the Riccati difference equation of optimal control.** / Iglesias, Pablo A.

Research output: Contribution to journal › Article

*Linear and Multilinear Algebra*, vol. 46, no. 4, pp. 313-326.

}

TY - JOUR

T1 - On the Riccati difference equation of optimal control

AU - Iglesias, Pablo A

PY - 1999

Y1 - 1999

N2 - Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

AB - Necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control are derived. The results are based on a recent spectral characterization of stabilizability which allow for the time-invariant derivation to go through mutatis mutandis. It is also shown that if the system's dynamics are antistable or observable, then the solution is positive-definite.

KW - Optimal control

KW - Riccati equations

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=0000285085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000285085&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000285085

VL - 46

SP - 313

EP - 326

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 4

ER -