### Abstract

In this paper we consider the problem of minimizing the l_{1} norm of the transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its H_{2} norm under a specified level. The problem is analysed for the discrete-time, SISO, linear time invariant case. It is shown that an optimal solution always exists. Duality theory is employed to show that any optimal solution is a finite impulse response sequence and an a priori bound is given on its length. The problem is reduced to a finite dimensional convex optimization problem with an a priori determined dimension. Finally it is shown that, in the region of interest of the H_{2} constraint level the optimal is unique and continuous with respect to changes in the constraint level.

Original language | English (US) |
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Pages (from-to) | 1438-1442 |

Number of pages | 5 |

Journal | Proceedings of the American Control Conference |

Volume | 2 |

State | Published - Jan 1 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA Duration: Jun 21 1995 → Jun 23 1995 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

_{1}/H

_{2}control.

*Proceedings of the American Control Conference*,

*2*, 1438-1442.