Exit problem and control theory
type: Item
instance of: scholarly article
title: Exit problem and control theory
zbMATH Open document ID: 0591.60050
DOI: 10.1016/0167-6911(85)90036-2
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The paper considers the Freidlin-Wentzell exit problem for systems of the form \(dx=f(x)dt+\epsilon \sigma dw_ t.\) The ''usual'' conditions (i) nondegeneracy of the noise, (ii) invariance of the basic domain D, (iii) the quasipotential attains its relative minimum at one point, are generalized to (a) controllability conditions on \(\dot y=f(y)+\sigma u\) (note: there is a misprint in equation (12)), (b) stability conditions on \(\dot z=f(z)\), (c) continuity requirements on the quasipotential. Then results on the exit rate and exit set hold similar to the Freidlin- Wentzell estimates. Linear systems \(dX=AXdt+\epsilon \sigma dw_ t\) are considered in more detail for stable matrices A, and applications to feedback stability of these systems are given.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 3949415
zbMATH Keywords: Freidlin-Wentzell exit problem
zbMATH Keywords: controllability conditions
zbMATH Keywords: stability conditions
zbMATH Keywords: continuity requirements on the quasipotential
zbMATH Keywords: stable matrices
zbMATH Keywords: feedback stability
author: Jerzy Zabczyk
reviewed by: Wolfgang Kliemann
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90036-2
OpenAlex ID: W1986298848
cites work: Stochastic Control for Small Noise Intensities
cites work: Stochastic calculus of variations and mechanics
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description: scientific article; zbMATH DE number 3949415