Open AccessStochastic suppression and stabilisation of non‐linear hybrid delay systems with general one‐sided polynomial growth condition and decay rate
Author(s) -
Zhu Song,
Sun Kaili,
Chang Wenting,
Wang Min
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0931
Subject(s) - control theory (sociology) , polynomial , term (time) , mathematics , hybrid system , brownian motion , brownian noise , noise (video) , diffusion , linear system , computer science , mathematical analysis , white noise , physics , statistics , control (management) , artificial intelligence , quantum mechanics , machine learning , image (mathematics) , thermodynamics
This study investigates the stochastic suppression and stabilisation of non‐linear hybrid delay systems with general one‐sided polynomial growth condition and decay rate. Given an unstable non‐linear hybrid delay systemx ˙ ( t ) =f ( x ( t ) ,x ( t − τ ( t ) ) ,r ( t ) , t ) with general one‐sided polynomial growth condition, the authors introduce two independent Brownian noise and perturb this system into stochastic hybrid delay system d x ( t ) =f ( x ( t ) ,x ( t − τ ( t ) ) , r ( t ) , t )d t + h( x ( t ) , r ( t ) , t )d B 1 ( t ) + g ( x ( t ) ,r ( t ) , t ) d B 2 ( t ) . It is shown that the non‐linear diffusion term g ( x ( t ) , r ( t ) , t ) may suppress the potential explosion of hybrid delay system. Under a stronger condition, another linear diffusion term h ( x ( t ) , r ( t ) , t ) will make the perturbed stochastic hybrid delay system is almost surely stable with general decay rate.