New Lyapunov conditions of stochastic finite-time stability and instability of nonlinear time-varying SDEs. Issue 6 (3rd June 2021)

• Record Type: Journal Article
• Authors: Yu, Xin; Yin, Juliang; Khoo, Suiyang
• Is Part Of: International journal of control. Volume 94:Issue 6(2021)
• Page Start: 1674
• Page End: 1681
• Publication Date: 2021-06-03
• Subjects: Stochastic finite-time stability -- instability -- multiple Lyapunov functions -- time-varying SDEs.; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2019.1662948
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : In this paper, we further consider the problem of stochastic finite-time stability and instability of nonlinear stochastic differential equations (SDEs) with time-varying drift and diffusion terms. The contributions of the paper are highlighted as follows. Some new conditions via multiple Lyapunov functions are given for stochastic finite-time stability of nonlinear time-varying SDEs. Compared with the existing results on stochastic finite-time stability, the constraint of the differential operator L V is further relaxed in this paper, which enable us to construct the Lyapunov functions much more easily in applications for nonlinear time-varying SDEs. In addition, a stochastic finite-time instability theorem is proposed, and it shows the necessity of lim t → ∞ ∫ t 0 t c ( s ) d s = ∞ in the proposed conditions of stochastic finite-time stability. Some examples are presented to illustrate the new results.