Abstract
In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
| Original language | English |
|---|---|
| Pages (from-to) | 2248-2259 |
| Number of pages | 12 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 65 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2006 Dec 15 |
| Externally published | Yes |
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Keywords
- Activation time ratio between stable and unstable subsystems
- Arbitrary switching
- Common Lyapunov function
- Stability
- Switched normal system
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Mathematics(all)
Cite this
Analysis and design of switched normal systems. / Zhai, Guisheng; Xu, Xuping; Lin, Hai; Michel, Anthony N.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 65, No. 12, 15.12.2006, p. 2248-2259.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analysis and design of switched normal systems
AU - Zhai, Guisheng
AU - Xu, Xuping
AU - Lin, Hai
AU - Michel, Anthony N.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
AB - In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
KW - Activation time ratio between stable and unstable subsystems
KW - Arbitrary switching
KW - Common Lyapunov function
KW - Stability
KW - Switched normal system
UR - http://www.scopus.com/inward/record.url?scp=33750974173&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33750974173&partnerID=8YFLogxK
U2 - 10.1016/j.na.2006.01.034
DO - 10.1016/j.na.2006.01.034
M3 - Article
AN - SCOPUS:33750974173
VL - 65
SP - 2248
EP - 2259
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 12
ER -