### 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 |
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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 1 |

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Michel, A. N., Zhai, G., Chen, X., & Sun, Y. (2004). ℒ

_{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.