### Abstract

In this paper, we study several qualitative properties for a class of switched systems composed of several subsystems, where each subsystem's vector field is composed of a linear time-invariant part and a nonlinear norm-bounded perturbation part. It is assumed that the linear subsystem matrices are commutative pairwise, and there exists a linear convex stable combination of unstable linear subsystem matrices. First, in the case of no perturbations, we propose a switching law under which the entire switched system is globally exponentially stable. In the switching law, Hurwitz stable sub-systems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. Secondly, under the same switching law, we analyze qualitative property of the switched system in the case where nonlinear norm-bounded perturbations exist. Some numerical examples are given in the paper to demonstrate the results.

Original language | English |
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Title of host publication | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |

Editors | S. Chunlin, S. Chunlin |

Pages | 139-144 |

Number of pages | 6 |

Publication status | Published - 2000 Dec 1 |

Externally published | Yes |

Event | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement - Guilin, China Duration: 2000 Jul 9 → 2000 Jul 12 |

### Publication series

Name | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |
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### Conference

Conference | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |
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Country | China |

City | Guilin |

Period | 00/7/9 → 00/7/12 |

### Keywords

- Commutative pairwise
- Exponential stability
- Nonlinear perturbations
- Switched system
- Switching law

### ASJC Scopus subject areas

- Engineering(all)

## Cite this

*Proceedings of the 4th Asia-Pacific Conference on Control and Measurement*(pp. 139-144). (Proceedings of the 4th Asia-Pacific Conference on Control and Measurement).