TY - JOUR
T1 - A note on multiple lyapunov functions and stability condition for switched and hybrid systems
AU - Zhai, Guisheng
AU - Matsune, Isatada
AU - Imae, Joe
AU - Kobayashi, Tomoaki
PY - 2009/5
Y1 - 2009/5
N2 - In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the ending points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.
AB - In this note, we consider stability condition with multiple Lyapunov functions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval of each subsystem, we propose a new Lyapunov stability condition, which complements the existing stability conditions that evaluate the value of multiple Lyapunov functions at the starting points or the ending points. We present several demonstrative examples, including the case where unstable subsystems are involved, and also apply the stability condition and the switching strategy to the switching control problem for stabilization of nonholonomic systems.
KW - Average value of multiple lyapunov functions
KW - Lyapunov stability
KW - Multiple Lyapunov functions
KW - Nonholonomic systems
KW - Switched and hybrid systems
KW - Switching strategy
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M3 - Article
AN - SCOPUS:63849246448
SN - 1349-4198
VL - 5
SP - 1189
EP - 1199
JO - International Journal of Innovative Computing, Information and Control
JF - International Journal of Innovative Computing, Information and Control
IS - 5
ER -