A survey of results and perspectives on stabilization of switched nonlinear systems with unstable modes

Abstract This paper surveys the recent theoretical results on the stabilization of switched nonlinear systems with unstable modes. Two cases are considered. (1) Some modes are stable, and others may be unstable. The stabilization can be achieved via the trade-off among stable modes and unstable ones. (2) All modes may be unstable. The stabilization can also be achieved via the trade-off among the potentially stable parts of all modes, or with the help of the jump dynamics at switching instants. The practical usefulness is illustrated by several applications including supervisory control, fault tolerant control, multi-agent systems, and networked control systems. Some perspectives are also provided.

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