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New criteria for stochastic suppression and stabilization of hybrid functional differential systems
Author(s) -
Zhu Song,
Shi Peng,
Lim ChengChew
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4114
Subject(s) - hybrid system , nonlinear system , brownian noise , control theory (sociology) , stochastic differential equation , mathematics , differential (mechanical device) , brownian motion , polynomial , noise (video) , computer science , mathematical analysis , white noise , physics , control (management) , statistics , quantum mechanics , machine learning , artificial intelligence , image (mathematics) , thermodynamics
Summary This paper establishes new criteria for stochastic suppression and stabilization of hybrid functional differential systems with general 1‐sided polynomial growth condition. For an unstable nonlinear hybrid functional differential system with general 1‐sided polynomial growth condition, 2 independent Brownian noise processes are used to perturb the system into the stochastic hybrid differential system. Theoretical analysis shows that one of the nonlinear diffusion terms may suppress the explosive solution of deterministic system, and the other one can make the perturbed hybrid system almost surely stable with general decay rate.