Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations

Abstract

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

“…Thus the proofs in this work are different from those in [16]. It should also be mentioned that the feedback control based on continuous state observation with a time delay was discussed in [25].…”

Conditions for local almost sure asymptotic stability

“…This strategy is widely known as stabilization by noise [1][2][3][4][5][6][7][8][9]. In general, the stability ensured by this strategy is global asymptotic stability in probability (global ASiP) [10,11], which is the most popular stability notion for the origin of a stochastic system.…”

Robust stabilization of hybrid uncertain stochastic systems by discrete‐time feedback control

“…Then Mao et al . in provided a better bound on the duration τ between two consecutive state observations and generalized the theory to a class of nonlinear hybrid stochastic systems, and You et al . weakened the global Lipschitz assumption on coefficients and further investigated the asymptotic stabilization of nonlinear hybrid stochastic systems.…”

“…It is observed that the discrete‐time feedback controls in are based on the discrete‐time observations of the state but they still depend on the continuous‐time observations of the mode. This is perfectly fine if the mode of the system is fully observable at no cost.…”