Some Improved Razumikhin Stability Criteria for Impulsive Stochastic Delay Differential Systems

• Published in: IEEE transactions on automatic control Vol. 64; no. 12; pp. 5207 - 5213
• Main Authors: Hu, Wei, Zhu, Quanxin, Karimi, Hamid Reza
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> p</tex-math> </inline-formula>th moment exponential stability; Asymptotic stability; Control theory; Delay; Delays; Impulsive stochastic delay differential system; Razumikhin condition; Razumikhin theorem; Stability criteria; Stochastic processes
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2911182

This paper is devoted to study the Razumikhin stability theorem for a class of impulsive stochastic delay differential systems. By developing a new lemma, stochastic analysis technique, and Razumikhin approach, several novel criteria of the pth moment exponential stability are derived for the related systems. The key feature of the criteria is that time-derivatives of the Razumikhin functions are allowed to be indefinite, which loosens the constraints of the existing results greatly. Finally, two examples are given to illustrate the usefulness and significance of the theoretical results.