### Abstract

We consider quadratic stabilizability and H_{∞} disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H_{∞} disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H_{∞} disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H_{∞} disturbance attenuation of the switched system.

Original language | English |
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Article number | 6426876 |

Pages (from-to) | 1935-1940 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

DOIs | |

Publication status | Published - 2012 Dec 1 |

Event | 51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 2012 Dec 10 → 2012 Dec 13 |

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### Keywords

- convex combination
- H disturbance attenuation
- LMI
- matrix inequalities
- output feedback
- quadratic stabilizability
- state feedback
- Switched linear systems

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization