### Abstract

In this paper, we study stability and ℒ
_{2} gain properties for a class of switched systems which are composed of normal discrete-time subsystems. When all subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching. For ℒ
_{2} gain analysis, we introduce an expanded matrix including each subsystem's coefficient matrices. Then, we show that if the expanded matrix is normal and Schur stable so that each subsystem is Schur stable and has unity ℒ
_{2} gain, then the switched normal system also has unity ℒ
_{2} gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ
_{2} gain.

Original language | English |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 3800-3805 |

Number of pages | 6 |

Volume | 6 |

Publication status | Published - 2005 |

Externally published | Yes |

Event | 2005 American Control Conference, ACC - Portland, OR, United States Duration: 2005 Jun 8 → 2005 Jun 10 |

### Other

Other | 2005 American Control Conference, ACC |
---|---|

Country | United States |

City | Portland, OR |

Period | 05/6/8 → 05/6/10 |

### Fingerprint

### Keywords

- Common quadratic lyapunov functions
- LMI
- Script L sign gain
- Stability
- Switched normal systems

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 6, pp. 3800-3805)

**Analysis of switched normal discrete-time systems.** / Zhai, Guisheng; Lin, Hai; Xuping, X. U.; Imae, Joe; Kobayashi, Tomoaki.

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

*Proceedings of the American Control Conference.*vol. 6, pp. 3800-3805, 2005 American Control Conference, ACC, Portland, OR, United States, 05/6/8.

}

TY - GEN

T1 - Analysis of switched normal discrete-time systems

AU - Zhai, Guisheng

AU - Lin, Hai

AU - Xuping, X. U.

AU - Imae, Joe

AU - Kobayashi, Tomoaki

PY - 2005

Y1 - 2005

N2 - In this paper, we study stability and ℒ 2 gain properties for a class of switched systems which are composed of normal discrete-time subsystems. When all subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching. For ℒ 2 gain analysis, we introduce an expanded matrix including each subsystem's coefficient matrices. Then, we show that if the expanded matrix is normal and Schur stable so that each subsystem is Schur stable and has unity ℒ 2 gain, then the switched normal system also has unity ℒ 2 gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ 2 gain.

AB - In this paper, we study stability and ℒ 2 gain properties for a class of switched systems which are composed of normal discrete-time subsystems. When all subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching. For ℒ 2 gain analysis, we introduce an expanded matrix including each subsystem's coefficient matrices. Then, we show that if the expanded matrix is normal and Schur stable so that each subsystem is Schur stable and has unity ℒ 2 gain, then the switched normal system also has unity ℒ 2 gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ 2 gain.

KW - Common quadratic lyapunov functions

KW - LMI

KW - Script L sign gain

KW - Stability

KW - Switched normal systems

UR - http://www.scopus.com/inward/record.url?scp=23944489800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944489800&partnerID=8YFLogxK

M3 - Conference contribution

VL - 6

SP - 3800

EP - 3805

BT - Proceedings of the American Control Conference

ER -