Almost sure exponential stabilization by stochastic feedback control based on discrete-time observations

Abstract

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 σ(t)x(δt)dB(t), and how to stabilize an unstable nonlinear hybrid SDE by controller G(r(δt))x(δt)dB(t), where δt 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.