### Abstract

Trade-offs between stability margin and performance are considered in two- and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively.

Original language | English (US) |
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Pages (from-to) | 1337-1366 |

Number of pages | 30 |

Journal | International Journal of Control |

Volume | 68 |

Issue number | 6 |

State | Published - Dec 1997 |

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### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*International Journal of Control*,

*68*(6), 1337-1366.

**Wiener-Hopf approach to trade-offs between stability margin and performance in two- and three-degree-of-freedom multivariable control systems.** / Bongiorno, J. J.; Khorrami, Farshad; Lin, T. C.

Research output: Contribution to journal › Article

*International Journal of Control*, vol. 68, no. 6, pp. 1337-1366.

}

TY - JOUR

T1 - Wiener-Hopf approach to trade-offs between stability margin and performance in two- and three-degree-of-freedom multivariable control systems

AU - Bongiorno, J. J.

AU - Khorrami, Farshad

AU - Lin, T. C.

PY - 1997/12

Y1 - 1997/12

N2 - Trade-offs between stability margin and performance are considered in two- and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively.

AB - Trade-offs between stability margin and performance are considered in two- and three-degree-of-freedom multivariable control systems using a Wiener-Hopf design approach. Maximum improvement in an approximate measure of stability margin is achieved at the expense of a prescribed increase in the quadratic cost functional measuring system performance. In order to attain an analytical solution to this fundamental trade-off problem, the approximate measure of stability margin chosen is also a quadratic cost function. A novel approach is introduced which allows structured perturbations in the coprime polynomial matrix fraction description of the plant transfer matrix to be taken into account. As a consequence, it is believed that the use of an approximate measure of stability margin is mitigated. Moreover, if needed, the solution obtained could serve as a very good initial one from which to search for better solutions iteratively.

UR - http://www.scopus.com/inward/record.url?scp=0031361557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031361557&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031361557

VL - 68

SP - 1337

EP - 1366

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 6

ER -