### Abstract

In this paper, we investigate the script L sign_{2} gain properties of time-controlled switched systems consisting of several linear Subsystems by using an average dwell time approach incorporated with a piecewise Lyapunov function. We show that when all subsystems are Hurwitz stable and have the script L sign_{2} gain smaller than a positive scalar γ_{0}, then the switched system can achieve any script L sign_{2} gain larger than γ_{0} if the average dwell time is chosen sufficiently large. The result is extended to the case where state jumps occur at switching points, and to a class of nonlinear switched systems by considering a Hamilton-Jacobi inequality for each subsystem.

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 | 145-149 |

Number of pages | 5 |

Publication status | Published - 2000 Dec 1 |

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

- Average dwell time
- Piecewise Lyapunov function
- Script L sign gain
- Switched system
- Switching law

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

_{2}gain analysis of switched systems with average dwell time. In S. Chunlin, & S. Chunlin (Eds.),

*Proceedings of the 4th Asia-Pacific Conference on Control and Measurement*(pp. 145-149). (Proceedings of the 4th Asia-Pacific Conference on Control and Measurement).