### 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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Pages (from-to) | 3800-3805 |

Number of pages | 6 |

Journal | Proceedings of the American Control Conference |

Volume | 6 |

Publication status | Published - 2005 Sep 1 |

Externally published | Yes |

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

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Proceedings of the American Control Conference*,

*6*, 3800-3805.