## Abstract

For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H_{∞} optimal control. Another measure of the gain of a system is the H_{2} norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H_{2} norm is bounded by the H_{∞} norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H_{∞} norm as a function of the H_{2} norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H_{2} norm can be bounded by a function of the H_{∞} norm and the bandwidth of the system.

Original language | English |
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Pages (from-to) | 173-181 |

Number of pages | 9 |

Journal | Systems and Control Letters |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 13 Feb 1995 |

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