### Abstract

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

Original language | English |
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Title of host publication | Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 |

Pages | 362-367 |

Number of pages | 6 |

Publication status | Published - 2006 Dec 1 |

Event | 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 - Ft. Lauderdale, FL, United States Duration: 2006 Apr 23 → 2006 Apr 25 |

### Publication series

Name | Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 |
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### Conference

Conference | 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 |
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Country | United States |

City | Ft. Lauderdale, FL |

Period | 06/4/23 → 06/4/25 |

### Keywords

- Arbitrary switching
- Common quadratic lyapunov (lyapunov-iike) functions
- Dwell time scheme
- Exponential stability
- Lie algebra
- Switched systems

### ASJC Scopus subject areas

- Computer Networks and Communications
- Control and Systems Engineering

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## Cite this

*Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06*(pp. 362-367). [1673173] (Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06).