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A Stability Result for Switched Systems With Multiple Equilibria

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Executive Summary

This paper studies stability properties of general switched systems with multiple distinct equilibria. It is shown that, if the dwell time of the switching events is greater than a certain lower bound, then the trajectory of a general switched system with multiple distinct equilibria, where each system is exponentially stable, globally converges to a superset of those equilibria and remains in that superset. A switched system consists of a family of continuous-time dynamical (sub) systems and a switching rule or signal that governs the switching between them. Switched systems, which are closely related to hybrid systems, are encountered in many applications ranging from mechanical and power systems to automotive and aerospace industries.

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