Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

Wenrui Li; Weiyin Fei; Yong Liang; Xuerong Mao

doi:10.1093/imamci/dnad008

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

Wenrui Li, Weiyin Fei, Yong Liang, Xuerong Mao

Mathematics And Statistics

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Abstract

We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.

Original language	English
Pages (from-to)	232-252
Number of pages	21
Journal	IMA Journal of Mathematical Control and Information
Volume	40
Issue number	2
DOIs	https://doi.org/10.1093/imamci/dnad008
Publication status	Published - 1 Jun 2023

Keywords

stabilize
destabilize
nonlinear hybrid systems
Levy noise
Periodic stochastic feedback control

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10.1093/imamci/dnad008

Li-etal-IMAJMCI-2023-Stabilization-and-destabilization-of-hybrid-systems-by-periodic-stochastic-controlsAccepted author manuscript, 302 KBLicence: Strath_1

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title = "Stabilization and destabilization of hybrid systems by periodic stochastic controls based on L{\'e}vy Noise",

abstract = "We focus in this paper on determining whether or not a periodic stochastic feedback control based on L{\'e}vy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with L{\'e}vy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on L{\'e}vy noise.",

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author = "Wenrui Li and Weiyin Fei and Yong Liang and Xuerong Mao",

year = "2023",

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doi = "10.1093/imamci/dnad008",

language = "English",

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TY - JOUR

T1 - Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

AU - Li, Wenrui

AU - Fei, Weiyin

AU - Liang, Yong

AU - Mao, Xuerong

PY - 2023/6/1

Y1 - 2023/6/1

N2 - We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.

AB - We focus in this paper on determining whether or not a periodic stochastic feedback control based on Lévy noise can stabilize or destabilize a given non-linear hybrid system. Using the Lyapunov functions and the periodic functions, we establish some sufficient conditions on the stability and instability for non-linear hybrid systems with Lévy noise. Moreover, we use some numerical examples and simulations to illustrate that an unstable (or stable) non-linear hybrid system can be stabilized (or destabilized) via periodic stochastic feedback control based on Lévy noise.

KW - stabilize

KW - destabilize

KW - nonlinear hybrid systems

KW - Levy noise

KW - Periodic stochastic feedback control

UR - https://academic.oup.com/imamci

U2 - 10.1093/imamci/dnad008

DO - 10.1093/imamci/dnad008

M3 - Article

SN - 0265-0754

VL - 40

SP - 232

EP - 252

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 2

ER -

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

Abstract

Keywords

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Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this

Stabilization and destabilization of hybrid systems by periodic stochastic controls based on Lévy Noise

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this