Almost sure stability of controlled degenerate diffusions

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dc.creatorBardi, Martino
dc.creatorCesaroni, Annalisa
dc.date2004-05-10
dc.date.accessioned2026-07-07T05:08:05Z
dc.date.available2026-07-07T05:08:05Z
dc.descriptionWe develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of Hamilton-Jacobi-Bellman partial differential inequality of $2nd$ order. We give local and global versions of the First and Second Lyapunov Theorems assuming the existence of a lower semicontinuous Lyapunov function satisfying such inequality in the viscosity sense. An explicit formula for a stabilizing feedback is provided for affine systems with smooth Lyapunov function. Several examples illustrate the theory.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0405167
dc.identifierhttp://arxiv.org/abs/math/0405167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71118
dc.subjectOptimization and Control
dc.subjectAnalysis of PDEs
dc.subject93E15, 49L25, 93D05, 93D20
dc.titleAlmost sure stability of controlled degenerate diffusions
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