### Abstract

Original language | English |
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Pages (from-to) | 646-659 |

Number of pages | 14 |

Journal | IEEE Transactions on Automatic Control |

Volume | 41 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 1996 |

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**Asymptotic behavior of the solution of the projection Riccati differential equation.** / Callier, F.M.; Winkin, J.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic behavior of the solution of the projection Riccati differential equation

AU - Callier, F.M.

AU - Winkin, J.J.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - The solution of the Riccati differential equation (RDE) is shown to be asymptotically close to the solution of the projection Riccati differential equation (PRDE). The asymptotic behavior of the latter is analyzed in an explicit formula. The almost-periodic asymptote of the solution of the PRDE is computed by an algorithm based upon the concepts of an aperiodic/almost-periodic generator (APG) decomposition of a linear map and unit row-staircase form of a polynomial matrix. The analysis ultimately provides a convergence criterion. In particular, it is shown that the solution of the PRDE always converges in the aperiodic case.

AB - The solution of the Riccati differential equation (RDE) is shown to be asymptotically close to the solution of the projection Riccati differential equation (PRDE). The asymptotic behavior of the latter is analyzed in an explicit formula. The almost-periodic asymptote of the solution of the PRDE is computed by an algorithm based upon the concepts of an aperiodic/almost-periodic generator (APG) decomposition of a linear map and unit row-staircase form of a polynomial matrix. The analysis ultimately provides a convergence criterion. In particular, it is shown that the solution of the PRDE always converges in the aperiodic case.

UR - http://www.scopus.com/inward/record.url?scp=0030150959&partnerID=8YFLogxK

U2 - 10.1109/9.489202

DO - 10.1109/9.489202

M3 - Article

AN - SCOPUS:0030150959

VL - 41

SP - 646

EP - 659

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 5

ER -