Abstract
AbstractThis paper formulates the notions of pivotal switching sequence and pivotal switched system as well as quasi-invariance to investigate ultimate motion of switched autonomous systems. The family of switching sequences that eventually drive the system motion is captured by pivotal switching sequences and the system ultimate motion is captured by pivotal switched systems through the quasi-invariance property of limit set. An invariance principle combining quasi-invariance property and Lyapunov functions for better estimate of resting region of system trajectories is introduced. An example of verifying the existence of limit cycle of a switched system using proposed invariance principle is provided.
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