### Abstract

This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

Original language | English |
---|---|

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 | 2174-2179 |

Number of pages | 6 |

DOIs | |

Publication status | Published - Dec 1 2009 |

Externally published | Yes |

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 |
---|---|

ISSN (Print) | 0191-2216 |

### Other

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

Country | China |

City | Shanghai |

Period | 12/15/09 → 12/18/09 |

### All Science Journal Classification (ASJC) codes

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

## Fingerprint Dive into the research topics of 'Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009*(pp. 2174-2179). [5399826] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399826