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On the p th moment integral input‐to‐state stability and input‐to‐state stability criteria for impulsive stochastic functional differential equations
Author(s) -
Hu Wei,
Zhu Quanxin,
Karimi Hamid Reza
Publication year - 2019
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.4688
Subject(s) - moment (physics) , stability (learning theory) , mathematics , state (computer science) , stochastic differential equation , differential (mechanical device) , differential equation , control theory (sociology) , mathematical analysis , computer science , control (management) , algorithm , artificial intelligence , engineering , physics , classical mechanics , machine learning , aerospace engineering
Summary In this paper, several new Razumikhin‐type theorems for impulsive stochastic functional differential equations are studied by applying stochastic analysis techniques and Razumikhin stability approach. By developing a new comparison principle for stochastic version, some novel criteria of the p th moment integral input‐to‐state stability and input‐to‐state stability are derived for the related systems. The feature of the criteria shows that time‐derivatives of the Razumikhin functions are allowed to be indefinite, even unbounded, which can loosen the constraints of the existing results. Finally, some examples are given to illustrate the usefulness and significance of the theoretical results.