Almost sure stability of controlled degenerate diffusions

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We 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.
26 pages

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Optimization and Control, Analysis of PDEs, 93E15, 49L25, 93D05, 93D20

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http://salesiana.dossiersoluciones.com/handle/123456789/71118

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405167
 http://arxiv.org/abs/math/0405167

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arXiv