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

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