Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion

• Published in: Systems & control letters Vol. 140; p. 104699
• Main Authors: Zhu, Quanxin, Huang, Tingwen
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2020
• Subjects: [formula omitted]th moment exponential stability; G-Brownian motion; Stochastic delay feedback control; Stochastic delay nonlinear system; Time-varying delay; Stochastic delay feedback control; pth moment exponential stability; Time-varying delay; Stochastic delay nonlinear system; G-Brownian motion
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2020.104699

This paper is devoted to study the pth moment exponential stability problem for a class of stochastic delay nonlinear systems (SDNSs) driven by G-Brownian motion. The delays considered in this paper are time-varying delays τi(t)∈[0,τ] (1≤i≤3) and they are not required to be differentiable. Different from the traditional methods, we use a new approach: stochastic delay feedback controls. We firstly compare the SDNS with the corresponding stochastic nonlinear system (SNS) instead of studying the stability of the SDNS directly. Then, we impose the condition on the SNS to ensure the pth moment exponential stability of the SNS. Furthermore, we show that there is a positive constant τ∗ such that the SDNS is also pth moment exponentially stable provided τ<τ∗. In particular, we give an implicit lower bound for τ∗ which can be computed numerically.