On Deterministic and Stochastic Sliding Modes via Small Diffusion Approximation

G.N. Milstein, A.Yu. Veretennikov

2000, v.6, №3, 371-396

ABSTRACT

We study solutions of a system of ordinary differential equations with discontinuity of its vector field on a smooth surface via small additive diffusion perturbations. When a diffusion term tends to zero, one obtains limiting sliding modes on the surface with explicit representation for its motion law. Stochastic sliding modes are also established.

Keywords: differential equations with discontinuous right-hand sides,sliding modes,stochastic differential equations,stochastic averaging principle

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