On the continuity of the Lyapunov functions in the converse stability theorems for discontinuous dynamical systems |
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Authors: | Ling Hou Anthony N Michel |
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Institution: | aDepartment of Electrical and Computer Engineering, St. Cloud State University, St. Cloud, MN 56301, USA;bDepartment of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | In H. Ye, A.N. Michel, L. Hou, Stability theory for hybrid dynamical systems, IEEE Transactions on Automatic Control 43 (4) (1998) 461–474] we established, among other results, a set of sufficient conditions for the uniform asymptotic stability of invariant sets for discontinuous dynamical systems (DDS) defined on metric space, and under some additional minor assumptions, we also established a set of necessary conditions (a converse theorem). This converse theorem involves Lyapunov functions which need not necessarily be continuous. In the present paper, we show that under some additional very mild assumptions, the Lyapunov functions for the converse theorem need actually be continuous. |
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Keywords: | Stability Lyapunov function Discontinuous dynamical system Converse theorem |
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