### Abstract

Poles and zeros are defined for continuous-time, linear, time-varying systems. A pole set for a time-varying state equation defines a stability-preserving variable change relating the original state equation to a time-varying, diagonal state equation. A zero is a function of time corresponding to an exponential input whose transmission to the output is blocked within the system. These definitions are shown to be generalizations of the definitions of poles and zeros in the time-invariant case. Using these definitions, it is shown that the relationship between the loss of controllability and/or observability in cascade systems and pole/zero cancellations is analogous to the relationship in the time-invariant case.

Original language | English (US) |
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Pages (from-to) | 103-130 |

Number of pages | 28 |

Journal | International Journal of Control |

Volume | 71 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1998 |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications

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## Cite this

*International Journal of Control*,

*71*(1), 103-130. https://doi.org/10.1080/002071798221957