### 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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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 1935-1940 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2012 |

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

### Other

Other | 51st IEEE Conference on Decision and Control, CDC 2012 |
---|---|

Country | United States |

City | Maui, HI |

Period | 12/12/10 → 12/12/13 |

### Fingerprint

### 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

### Cite this

_{∞}disturbance attenuation of switched linear systems via state and output feedback In

*Proceedings of the IEEE Conference on Decision and Control*(pp. 1935-1940). [6426876] https://doi.org/10.1109/CDC.2012.6426876

**Quadratic stabilizability and H
_{∞} disturbance attenuation of switched linear systems via state and output feedback
.** / Zhai, Guisheng.

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

_{∞}disturbance attenuation of switched linear systems via state and output feedback in

*Proceedings of the IEEE Conference on Decision and Control.*, 6426876, pp. 1935-1940, 51st IEEE Conference on Decision and Control, CDC 2012, Maui, HI, United States, 12/12/10. https://doi.org/10.1109/CDC.2012.6426876

_{∞}disturbance attenuation of switched linear systems via state and output feedback In Proceedings of the IEEE Conference on Decision and Control. 2012. p. 1935-1940. 6426876 https://doi.org/10.1109/CDC.2012.6426876

}

TY - GEN

T1 - Quadratic stabilizability and H ∞ disturbance attenuation of switched linear systems via state and output feedback

AU - Zhai, Guisheng

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - convex combination

KW - H disturbance attenuation

KW - LMI

KW - matrix inequalities

KW - output feedback

KW - quadratic stabilizability

KW - state feedback

KW - Switched linear systems

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UR - http://www.scopus.com/inward/citedby.url?scp=84874228921&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6426876

DO - 10.1109/CDC.2012.6426876

M3 - Conference contribution

SP - 1935

EP - 1940

BT - Proceedings of the IEEE Conference on Decision and Control

ER -