### Abstract

This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not necessarily polynomial), the worst-case expected value can be approximated by using its polynomial approximations. Moreover, the proposed approach is applied to compute hard bounds of the worst-case probability of a polynomial being negative. Numerical examples are presented which illustrate the application of the results in this paper.

Original language | English (US) |
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Title of host publication | Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 |

Pages | 1151-1156 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2009 |

Event | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Other

Other | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 |
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Country | China |

City | Shanghai |

Period | 12/15/09 → 12/18/09 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009*(pp. 1151-1156). [5399737] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399737