Some properties of finite-time stable stochastic nonlinear systems

Yin, J., Ding, D., Liu, Z. and Khoo, S. 2015, Some properties of finite-time stable stochastic nonlinear systems, Applied mathematics and computation, vol. 259, pp. 686-697, doi: 10.1016/j.amc.2015.02.088.

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Title Some properties of finite-time stable stochastic nonlinear systems
Author(s) Yin, J.
Ding, D.
Liu, Z.
Khoo, S.
Journal name Applied mathematics and computation
Volume number 259
Start page 686
End page 697
Total pages 12
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2015-05-15
ISSN 0096-3003
Keyword(s) Continuous dependence theorems
Finite-time stochastic stability
Lyapunov theorem
Stochastic nonlinear systems
Stochastic settling time
Science & Technology
Physical Sciences
Mathematics, Applied
Converse Lyapunov theorem
Summary In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.
Language eng
DOI 10.1016/j.amc.2015.02.088
Field of Research 090602 Control Systems, Robotics and Automation
010203 Calculus of Variations, Systems Theory and Control Theory
Socio Economic Objective 970109 Expanding Knowledge in Engineering
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Elsevier
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Document type: Journal Article
Collection: School of Engineering
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