### Abstract

The problem of mixed H_{2}/H_{∞} control with pole placement is considered for linear time-invariant systems. This is the problem of determining a controller for linear time-invariant systems which minimizes the H_{2}-norm of a certain closed-loop transfer function subject to an H_{∞}-norm constraint on another closed-loop transfer function and an additional constraint on the location of the closed-loop poles in the complex plane. An optimization problem is posed for the pole-constrained H_{2}/H_{∞} problem in such a way that the objective function is expressed as a weighted sum of the actual H_{2} cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H_{2} performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.

Original language | English |
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Pages (from-to) | 151-173 |

Number of pages | 23 |

Journal | Optimal Control Applications and Methods |

Volume | 15 |

Issue number | 3 |

Publication status | Published - 1994 Jul |

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### ASJC Scopus subject areas

- Management Science and Operations Research
- Control and Systems Engineering
- Applied Mathematics
- Control and Optimization

### Cite this

_{2}/H

_{∞}control with pole placement in a class of regions.

*Optimal Control Applications and Methods*,

*15*(3), 151-173.