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 |
|---|---|
| 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 |
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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
Cite this
Quadratic stabilizability and H ∞ disturbance attenuation of switched linear systems via state and output feedback . / Zhai, Guisheng.
Proceedings of the IEEE Conference on Decision and Control. 2012. p. 1935-1940 6426876.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
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
UR - http://www.scopus.com/inward/record.url?scp=84874228921&partnerID=8YFLogxK
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
AN - SCOPUS:84874228921
SP - 1935
EP - 1940
BT - Proceedings of the IEEE Conference on Decision and Control
ER -