### 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) |
---|---|

Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | IEEE |

Pages | 505-508 |

Number of pages | 4 |

State | Published - 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 505-508). IEEE.

**SELECTION OF THE WEIGHTING MATRICES AND THE DEGREE OF RELATIVE STABILITY TO POSITION THE SPECTRUM OF THE OPTIMAL REGULATOR.** / Medanic, J.; Tharp, Hal S; Perkins, W. R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

}

TY - GEN

T1 - SELECTION OF THE WEIGHTING MATRICES AND THE DEGREE OF RELATIVE STABILITY TO POSITION THE SPECTRUM OF THE OPTIMAL REGULATOR.

AU - Medanic, J.

AU - Tharp, Hal S

AU - Perkins, W. R.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023011117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023011117&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0023011117

SP - 505

EP - 508

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

ER -