### Abstract

New properties of the algebraic Riccati equation (ARE) are developed, establishing the invariance of certain eigenspaces of the associated Hamiltonian matrix to certain perturbations of the weighting matrix Q and the degree of relative stability. These results are used to develop a sequential procedure which, by modifying the performance criterion, achieves full and numerically convenient placement of the real parts of the optimal eigenvalues. The placement of eigenvalues is implicit since the invariance results specify the final performance criterion; the solution of the resulting linear-quadratic problem then defines the optimal gain and the closed-loop system having the desired spectral configuration.

Original language | English (US) |
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Pages (from-to) | 505-508 |

Number of pages | 4 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

State | Published - Dec 1 1986 |

Externally published | Yes |

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*Proceedings of the IEEE Conference on Decision and Control*, 505-508.