### Abstract

Results on the stability region of a class of nonlinear systems and the number of equilibrium points on its boundary are derived. Concepts such as general position and regularity of stability regions are developed. Based on these two conditions, together with the general topological arguments, the lower bound and upper bound on the number of unstable equilibrium points are obtained. These bounds can be used to estimate the computational load required to construct the stability boundary.

Original language | English |
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Pages (from-to) | 889-894 |

Number of pages | 6 |

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

Publication status | Published - 1 Dec 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

**ON THE NUMBER OF UNSTABLE EQUILIBRIUM POINTS OF A CLASS OF NONLINEAR SYSTEMS.** / Luxemburg, L. A.; Huang, Garng Morton.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, pp. 889-894.

}

TY - JOUR

T1 - ON THE NUMBER OF UNSTABLE EQUILIBRIUM POINTS OF A CLASS OF NONLINEAR SYSTEMS.

AU - Luxemburg, L. A.

AU - Huang, Garng Morton

PY - 1987/12/1

Y1 - 1987/12/1

N2 - Results on the stability region of a class of nonlinear systems and the number of equilibrium points on its boundary are derived. Concepts such as general position and regularity of stability regions are developed. Based on these two conditions, together with the general topological arguments, the lower bound and upper bound on the number of unstable equilibrium points are obtained. These bounds can be used to estimate the computational load required to construct the stability boundary.

AB - Results on the stability region of a class of nonlinear systems and the number of equilibrium points on its boundary are derived. Concepts such as general position and regularity of stability regions are developed. Based on these two conditions, together with the general topological arguments, the lower bound and upper bound on the number of unstable equilibrium points are obtained. These bounds can be used to estimate the computational load required to construct the stability boundary.

UR - http://www.scopus.com/inward/record.url?scp=0023542583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023542583&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0023542583

SP - 889

EP - 894

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -