### Abstract

In this paper, we study ℒ_{2} gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the ℒ_{2} gain less than 7, we discuss the ℒ_{2} gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in ℒ_{2} sense, and show that the switched system has the ℒ_{2} gain less than the same level 7 under arbitrary switching. As an example in this case, we analyze switched symmetric systems and derive the common Lyapunov function clearly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in ℒ_{2} sense, and show that the switched system achieves an ultimate (or weighted) ℒ_{2} gain under an average dwell time scheme.

Original language | English |
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Title of host publication | Proceedings of the SICE Annual Conference |

Pages | 2483-2488 |

Number of pages | 6 |

Publication status | Published - 2004 |

Externally published | Yes |

Event | SICE Annual Conference 2004 - Sapporo Duration: 2004 Aug 4 → 2004 Aug 6 |

### Other

Other | SICE Annual Conference 2004 |
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City | Sapporo |

Period | 04/8/4 → 04/8/6 |

### Fingerprint

### Keywords

- ℒ gain
- Average dwell time
- Common Lyapunov function
- Piecewise Lyapunov function
- Switched system

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

_{2}gain analysis for switched systems with continuous-time and discrete-time subsystems. In

*Proceedings of the SICE Annual Conference*(pp. 2483-2488). [FPI-10-4]

**ℒ _{2} gain analysis for switched systems with continuous-time and discrete-time subsystems.** / Zhai, Guisheng; Lin, Hai; Kim, Youngbok.

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

_{2}gain analysis for switched systems with continuous-time and discrete-time subsystems. in

*Proceedings of the SICE Annual Conference.*, FPI-10-4, pp. 2483-2488, SICE Annual Conference 2004, Sapporo, 04/8/4.

_{2}gain analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the SICE Annual Conference. 2004. p. 2483-2488. FPI-10-4

}

TY - GEN

T1 - ℒ2 gain analysis for switched systems with continuous-time and discrete-time subsystems

AU - Zhai, Guisheng

AU - Lin, Hai

AU - Kim, Youngbok

PY - 2004

Y1 - 2004

N2 - In this paper, we study ℒ2 gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the ℒ2 gain less than 7, we discuss the ℒ2 gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in ℒ2 sense, and show that the switched system has the ℒ2 gain less than the same level 7 under arbitrary switching. As an example in this case, we analyze switched symmetric systems and derive the common Lyapunov function clearly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in ℒ2 sense, and show that the switched system achieves an ultimate (or weighted) ℒ2 gain under an average dwell time scheme.

AB - In this paper, we study ℒ2 gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the ℒ2 gain less than 7, we discuss the ℒ2 gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in ℒ2 sense, and show that the switched system has the ℒ2 gain less than the same level 7 under arbitrary switching. As an example in this case, we analyze switched symmetric systems and derive the common Lyapunov function clearly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in ℒ2 sense, and show that the switched system achieves an ultimate (or weighted) ℒ2 gain under an average dwell time scheme.

KW - ℒ gain

KW - Average dwell time

KW - Common Lyapunov function

KW - Piecewise Lyapunov function

KW - Switched system

UR - http://www.scopus.com/inward/record.url?scp=12744254953&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12744254953&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:12744254953

SP - 2483

EP - 2488

BT - Proceedings of the SICE Annual Conference

ER -