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Exponential ultimate boundedness of impulsive stochastic delay difference systems
Author(s) -
Xu Liguang,
Hu Hongxiao,
Ge Shuzhi Sam
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.3901
Subject(s) - mathematics , bounded function , exponential function , algebraic number , uniform boundedness , control theory (sociology) , exponential stability , convergence (economics) , rate of convergence , moment (physics) , lyapunov function , computer science , mathematical analysis , control (management) , nonlinear system , computer network , channel (broadcasting) , physics , classical mechanics , quantum mechanics , artificial intelligence , economics , economic growth
Summary This paper is concerned with the exponential ultimate boundedness problems for the impulsive stochastic delay difference systems. Several sufficient conditions on the global p th moment exponential ultimate boundedness are presented by using the Lyapunov methods and the algebraic inequality techniques, and the estimated exponential convergence rate and the ultimate bound are provided as well. As an application, the boundedness criteria are applied to a class of discrete impulsive stochastic neural networks with delays. The obtained results show that the impulses not only can stabilize an unstable stochastic difference delay system but also can make an unbounded stochastic difference delay system into a bounded system. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.