*(English)*Zbl 0883.93024

Various (dynamical) feedback design problems for linear time invariant control systems are discussed and solved in terms of linear matrix inequalities (LMI’s).

After the introduction, which gives a good motivation for the chosen approach, the authors derive LMI-formulations for various feedback control objectives: ${H}_{\infty}$ control, general quadratic constraints, (generalized) ${H}_{2}$ control, peak impulse response, regional pole constraints and robust regulation.

The LMI approach is then shown to provide a synthesis approach in which several of these objectives can be combined where for each of the mentioned topics, both the LMI formulation and the corresponding feedback synthesis (for full order systems) are given in detail in a “Catalog of LMI’s”. Finally the reduced order case is briefly mentioned and two examples are discussed.

##### MSC:

93B50 | Synthesis problems |

15A39 | Linear inequalities of matrices |

93B52 | Feedback control |

93B55 | Pole and zero placement problems |

93B36 | ${H}^{\infty}$-control |