### Abstract

We propose a definition of almost Toeplitz matrices as matrices with off-diagonal decay that are close to begin Toeplitz in their center columns and decrease in Toeplitzness toward their first and last columns. We prove that such matrices form an operator algebra under matrix addition and multiplication. We use this framework to show that algebraic Riccati equations with almost Toeplitz coefficient matrices have almost Toeplitz solutions.

Original language | English (US) |
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Title of host publication | 2009 American Control Conference, ACC 2009 |

Pages | 854-859 |

Number of pages | 6 |

DOIs | |

State | Published - Nov 23 2009 |

Event | 2009 American Control Conference, ACC 2009 - St. Louis, MO, United States Duration: Jun 10 2009 → Jun 12 2009 |

### Publication series

Name | Proceedings of the American Control Conference |
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ISSN (Print) | 0743-1619 |

### Other

Other | 2009 American Control Conference, ACC 2009 |
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Country | United States |

City | St. Louis, MO |

Period | 6/10/09 → 6/12/09 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

Fardad, M. (2009). The operator algebra of almost toeplitz matrices and the optimal control of large-scale systems. In

*2009 American Control Conference, ACC 2009*(pp. 854-859). [5160148] (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2009.5160148