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Asymptotic stability in probability for discrete‐time stochastic coupled systems on networks with multiple dispersal
Author(s) -
Wang Pengfei,
Hong Yu,
Su Huan
Publication year - 2017
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.3927
Subject(s) - lyapunov function , discrete time and continuous time , stability (learning theory) , mathematics , convergence (economics) , graph , probability density function , computer science , control theory (sociology) , mathematical optimization , topology (electrical circuits) , discrete mathematics , nonlinear system , combinatorics , control (management) , physics , statistics , quantum mechanics , machine learning , artificial intelligence , economics , economic growth
Summary In this paper, we consider the asymptotic stability in probability for discrete‐time stochastic coupled systems on networks with multiple dispersal (DSCSM). We begin with modeling a DSCSM on multiple digraphs and consequently construct a global Lyapunov function based on the topological structure of multiple digraphs. Using the Lyapunov method combined with the graph theory and the supermartingale convergence theorem, several stability criteria for DSCSM are derived. In what follows, the given results are utilized to analyze a stochastic coupled oscillator model. Finally, 2 numerical examples are also given to demonstrate the feasibility of the proposed results.