2010
DOI: 10.1090/s0002-9939-2010-10298-8
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Some properties of Lyapunov function sets

Abstract: Abstract. The purpose of this paper is to study some geometrical and topological properties of Lyapunov function sets. These functions are very useful in control theory to solve stability problems. We focus our attention on the set of Lyapunov functions associated with continuous and discontinuous nonlinear systems.

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Cited by 2 publications
(1 citation statement)
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“…Convexity in the context of Lyapunov stability theory has been an active research area. For example, convexity in linear optimal control [LR95], convexity in the dual density formulation due to Rantzer [PPR04] and convexity of the set of Lyapunov functions due to Moulay [Mou10]. We are, however, interested in understanding convexity of Lyapunov functions themselves.…”
Section: On Convexity and Continuationmentioning
confidence: 99%
“…Convexity in the context of Lyapunov stability theory has been an active research area. For example, convexity in linear optimal control [LR95], convexity in the dual density formulation due to Rantzer [PPR04] and convexity of the set of Lyapunov functions due to Moulay [Mou10]. We are, however, interested in understanding convexity of Lyapunov functions themselves.…”
Section: On Convexity and Continuationmentioning
confidence: 99%