### Abstract

In the last few years some articles have emphasized certain fundamental inconsistencies underlying feedback control theory. The paper of Willems [1] Georgiou and Smith [2], later the works of Makila [3],[4], of Leithead et al. [5] have stressed the inconsistency of standard formalisms of linear time-invariant systems when the signals are double sided and the systems are open loop unstable. We establish a framework for a consistent time domain and frequency domain representation of discrete time linear time-invariant systems and, furthermore, that supports the consistent analysis of discrete time linear time-invariant feedback systems when signals are double sided and the systems are open loop unstable.

Original language | English |
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Title of host publication | Switching and Learning in Feedback Systems |

Publisher | Springer-Verlag |

Pages | 273-289 |

Number of pages | 16 |

ISBN (Print) | 978-3-540-24457-8 |

DOIs | |

Publication status | Published - 2005 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 3355 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Keywords

- feedback control theory
- linear time-invariant systems

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## Cite this

Ragnoli, E., & Leithead, W. E. (2005). Reconciliation of inconsistencies in the theory of linear systems. In

*Switching and Learning in Feedback Systems*(pp. 273-289). (Lecture Notes in Computer Science; Vol. 3355). Springer-Verlag. https://doi.org/10.1007/978-3-540-30560-6_12