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

Mao, Xuerong and Liu, Wei and Hu, Liangjian and Luo, Qi and Lu, Jianqiu (2014) Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations. Systems and Control Letters, 73. pp. 88-95. ISSN 0167-6911 (https://doi.org/10.1016/j.sysconle.2014.08.011)

[thumbnail of Mao-etal-SCL2014-stablization-of-hybrid-stochastic-differential-equestions-by-feedback] PDF. Filename: Mao_etal_SCL2014_stablization_of_hybrid_stochastic_differential_equestions_by_feedback.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo

Download (419kB)

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.