### Abstract

Motivated by recent drastic advances in the study of linear-time invariant (ETI) positive systems, we explore analysis techniques of general, not necessarily positive ETI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general ETI system analysis. A typical example is the computation of the H_{2} norm where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an ETI system whose impulse response is given by the product of impulse responses of two different ETI systems. Then, as the main result, we reduce the H_{2} norm computation problem of a general ETI system into the L_{∞}-induced norm computation problem (or L_{1} problem in short) of a positive system, by which we can derive a closed-form formula for the H_{∞} norm computation.

Original language | English |
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Title of host publication | 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1216-1219 |

Number of pages | 4 |

ISBN (Electronic) | 9784907764579 |

DOIs | |

Publication status | Published - Nov 10 2017 |

Externally published | Yes |

Event | 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017 - Kanazawa, Japan Duration: Sep 19 2017 → Sep 22 2017 |

### Publication series

Name | 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017 |
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Volume | 2017-November |

### Other

Other | 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017 |
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Country | Japan |

City | Kanazawa |

Period | 9/19/17 → 9/22/17 |

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Control and Optimization
- Control and Systems Engineering
- Instrumentation

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## Cite this

*2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017*(pp. 1216-1219). (2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2017; Vol. 2017-November). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/SICE.2017.8105544