Abstract
In this paper, we study stability and L2 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 L2 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 L2 gain, then the switched normal system also has unity L2 gain under arbitrary switching. The key point is establishing a common quadratic Lyapunov function for all subsystems in the sense of unity L2 gain.
| Original language | English |
|---|---|
| Pages (from-to) | 1788-1799 |
| Number of pages | 12 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 66 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2007 Apr 15 |
| Externally published | Yes |
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Keywords
- Common quadratic Lyapunov functions
- L gain
- LMI
- Stability
- Switched normal systems
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Mathematics(all)
Cite this
Analysis of switched normal discrete-time systems. / Zhai, Guisheng; Lin, Hai; Xu, Xuping; Imae, Joe; Kobayashi, Tomoaki.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 66, No. 8, 15.04.2007, p. 1788-1799.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analysis of switched normal discrete-time systems
AU - Zhai, Guisheng
AU - Lin, Hai
AU - Xu, Xuping
AU - Imae, Joe
AU - Kobayashi, Tomoaki
PY - 2007/4/15
Y1 - 2007/4/15
N2 - In this paper, we study stability and L2 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 L2 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 L2 gain, then the switched normal system also has unity L2 gain under arbitrary switching. The key point is establishing a common quadratic Lyapunov function for all subsystems in the sense of unity L2 gain.
AB - In this paper, we study stability and L2 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 L2 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 L2 gain, then the switched normal system also has unity L2 gain under arbitrary switching. The key point is establishing a common quadratic Lyapunov function for all subsystems in the sense of unity L2 gain.
KW - Common quadratic Lyapunov functions
KW - L gain
KW - LMI
KW - Stability
KW - Switched normal systems
UR - http://www.scopus.com/inward/record.url?scp=33846623729&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846623729&partnerID=8YFLogxK
U2 - 10.1016/j.na.2006.02.024
DO - 10.1016/j.na.2006.02.024
M3 - Article
VL - 66
SP - 1788
EP - 1799
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 8
ER -