On Duality for Lyapunov Functions of Nonstrict Convex Processes
Jaap Eising, M. Kanat Camlibel
TL;DR
This paper introduces a new definition of Lyapunov functions for difference inclusions based on convex processes, improving stability analysis and establishing duality relationships.
Contribution
It proposes a novel Lyapunov function definition for convex processes and explores conditions linking weak and strong Lyapunov functions via duality.
Findings
Better reflection of stability properties for nonstrict convex processes
Conditions under which weak Lyapunov functions imply strong dual Lyapunov functions
Enhanced understanding of duality in stability analysis
Abstract
This paper provides a novel definition for Lyapunov functions for difference inclusions defined by convex processes. It is shown that this definition reflects stability properties of nonstrict convex processes better than previously used definitions. In addition the paper presents conditions under which a weak Lyapunov function for a convex process yields a strong Lyapunov function for the dual of the convex process.
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