Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function

Lie Liu, Xuerong Mao, Jinde Cao

Research output: Contribution to journalArticle

Abstract

This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.
LanguageEnglish
Pages1986-2006
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume479
Issue number2
Early online date16 Jul 2019
DOIs
Publication statusE-pub ahead of print - 16 Jul 2019

Fingerprint

Vector Lyapunov Functions
Lyapunov functions
Differential System
Exponential Stability
Theorem
Razumikhin Technique
Stochastic Analysis
Asymptotic stability
Sufficient
Moment
Zero
Demonstrate

Keywords

  • vector Lyapunov function
  • razumikhin-type theorems
  • input-to-state stability
  • exponential stability
  • stochastic functional differential equation

Cite this

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abstract = "This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.",
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Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function. / Liu, Lie; Mao, Xuerong; Cao, Jinde.

In: Journal of Mathematical Analysis and Applications, Vol. 479, No. 2, 15.11.2019, p. 1986-2006.

Research output: Contribution to journalArticle

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AB - This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.

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KW - razumikhin-type theorems

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