Finite-time state-feedback control for a class of stochastic high-order nonlinear systems

Abstract

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.

Keywords:

• stochastic nonlinear systems
• adding one power integrator
• finite-time stability

2010 AMS Subject Classifications:

• 60H10
• 60H35
• 91B70

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (61104068, 61273119), Research Fund for the Doctoral Program of Higher Education of China (20090092120027, 20110092110021), Natural Science Foundation of Jiangsu Province (BK2010200), China Postdoctoral Science Foundation Funded Project (2012M511176) and the Fundamental Research Funds for the Central Universities (2242013R30006).