### 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 |

Externally published | Yes |

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

### Other

Other | Proceedings of the 4th Asia-Pacific Conference on Control and Measurement |
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City | Guilin |

Period | 00/7/9 → 00/7/12 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

### 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)

**Script L sign _{2} gain analysis of switched systems with average dwell time.** / Zhai, Guisheng; Hu, Bo; Yasuda, Kazunori; Michel, Anthony N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

_{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, Guilin, 00/7/9.

_{2}gain analysis of switched systems with average dwell time. In Chunlin S, Chunlin S, editors, Proceedings of the 4th Asia-Pacific Conference on Control and Measurement. 2000. p. 145-149

}

TY - GEN

T1 - Script L sign2 gain analysis of switched systems with average dwell time

AU - Zhai, Guisheng

AU - Hu, Bo

AU - Yasuda, Kazunori

AU - Michel, Anthony N.

PY - 2000

Y1 - 2000

N2 - In this paper, we investigate the script L sign2 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 sign2 gain smaller than a positive scalar γ0, then the switched system can achieve any script L sign2 gain larger than γ0 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.

AB - In this paper, we investigate the script L sign2 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 sign2 gain smaller than a positive scalar γ0, then the switched system can achieve any script L sign2 gain larger than γ0 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.

KW - Average dwell time

KW - Piecewise Lyapunov function

KW - Script L sign gain

KW - Switched system

KW - Switching law

UR - http://www.scopus.com/inward/record.url?scp=0034590769&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034590769&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0034590769

SN - 7801346955

SP - 145

EP - 149

BT - Proceedings of the 4th Asia-Pacific Conference on Control and Measurement

A2 - Chunlin, S.

A2 - Chunlin, S.

ER -