### Abstract

In this paper, we study ℒ_{2} gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ_{2} gain γ in the sense of satisfying an LMI, the switched system has the same ℒ_{2} gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ_{2} gain.

Original language | English |
---|---|

Pages (from-to) | 219-232 |

Number of pages | 14 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |

Volume | 11 |

Issue number | 2-3 |

Publication status | Published - 2004 Apr |

Externally published | Yes |

### Fingerprint

### Keywords

- ℒ gain
- Arbitrary switching
- Common Lyapunov function
- Linear matrix inequality (LMI)
- Switched symmetric system
- Time delay

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

_{2}gain analysis of switched symmetric systems with time delays.

*Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis*,

*11*(2-3), 219-232.

**ℒ _{2} gain analysis of switched symmetric systems with time delays.** / Michel, Anthony N.; Zhai, Guisheng; Chen, Xinkai; Sun, Ye.

Research output: Contribution to journal › Article

_{2}gain analysis of switched symmetric systems with time delays',

*Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis*, vol. 11, no. 2-3, pp. 219-232.

_{2}gain analysis of switched symmetric systems with time delays. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis. 2004 Apr;11(2-3):219-232.

}

TY - JOUR

T1 - ℒ2 gain analysis of switched symmetric systems with time delays

AU - Michel, Anthony N.

AU - Zhai, Guisheng

AU - Chen, Xinkai

AU - Sun, Ye

PY - 2004/4

Y1 - 2004/4

N2 - In this paper, we study ℒ2 gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ2 gain γ in the sense of satisfying an LMI, the switched system has the same ℒ2 gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ2 gain.

AB - In this paper, we study ℒ2 gain property for a class of switched systems which are composed of a finite number of linear time-invariant (LTI) symmetric subsystems with time delays in system states. We show that when all subsystems have ℒ2 gain γ in the sense of satisfying an LMI, the switched system has the same ℒ2 gain γ under arbitrary switching. The key idea is to establish a common Lyapunov function for all subsystems in the sense of ℒ2 gain.

KW - ℒ gain

KW - Arbitrary switching

KW - Common Lyapunov function

KW - Linear matrix inequality (LMI)

KW - Switched symmetric system

KW - Time delay

UR - http://www.scopus.com/inward/record.url?scp=4644350803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644350803&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 219

EP - 232

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

SN - 1201-3390

IS - 2-3

ER -