Journal
STOCHASTIC ANALYSIS AND APPLICATIONS
Volume 36, Issue 4, Pages 561-583Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/07362994.2018.1433046
Keywords
Stochastic feedback control; Markov chain; almost sure exponential stabilization; Brownian motion; discrete-time observations
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Funding
- University of Strathclyde [201577584]
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Since Mao initiated the study of stabilization of ordinary differential equations (ODEs) by stochastic feedback controls based on discrete-time state observations in 2016, no more work on this intriguing topic has been reported. This article investigates how to stabilize a given unstable linear non-autonomous ODE by controller sigma(t)x((t))dB(t), and how to stabilize an unstable nonlinear hybrid SDE by controller G(r((t)))x((t))dB(t), where (t) represents time points of observation with sufficiently small observation interval, B(t) is a Brownian motion and r(t) is the Markov Chain, in the sense of pth moment (0 < p < 1) and almost sure exponential stability.
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