TY - JOUR
T1 - Stabilization of highly nonlinear hybrid systems driven by Lévy noise and delay feedback control based on discrete-time state observations
AU - Moualkia, Seyfeddine
AU - Xu, Yong
N1 - Publisher Copyright:
© 2022 The Franklin Institute
PY - 2023/1
Y1 - 2023/1
N2 - There are many hybrid stochastic differential equations (SDEs) in the real-world that don't satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.
AB - There are many hybrid stochastic differential equations (SDEs) in the real-world that don't satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.
UR - http://www.scopus.com/inward/record.url?scp=85145590431&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2022.12.001
DO - 10.1016/j.jfranklin.2022.12.001
M3 - 文章
AN - SCOPUS:85145590431
SN - 0016-0032
VL - 360
SP - 1005
EP - 1035
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 2
ER -