TY - JOUR
T1 - Lie Algebraic Stability Analysis for Switched Systems With Continuous-Time and Discrete-Time Subsystems
AU - Zhai, Guisheng
AU - Imae, Joe
AU - Kobayashi, Tomoaki
AU - Liu, Derong
PY - 2006/2
Y1 - 2006/2
N2 - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all continuous-time subsystems are Hurwitz stable, all discrete-time subsystems are Schur stable, and furthermore the obtained Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.
AB - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all continuous-time subsystems are Hurwitz stable, all discrete-time subsystems are Schur stable, and furthermore the obtained Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.
KW - Arbitrary switching
KW - Lie algebra
KW - common quadratic Lyapunov functions
KW - continuous-time
KW - discrete-time
KW - exponential stability
KW - switched systems
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U2 - 10.1109/TCSII.2005.856033
DO - 10.1109/TCSII.2005.856033
M3 - Article
AN - SCOPUS:33144467772
SN - 1549-7747
VL - 53
SP - 152
EP - 156
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
IS - 2
ER -