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Stabilization for a class of stochastic nonlinear systems with arbitrary switching via the common Lyapunov function method

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Abstract

This paper addresses the stabilization problem for a class of stochastic nonlinear systems with arbitrary switching. Based on the simultaneous domination approach, the common Lyapunov function method and the backstepping technique, a state feedback controller and an output feedback controller are designed, respectively. The closed-loop systems are proved to be globally asymptotically stable in probability. The main advantage of the proposed control schemes is that the controllers are independent of switching signal. Two simulation examples are given to illustrate the effectiveness of the proposed control strategies.

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Correspondence to Jian Wu.

Additional information

Recommended by Editorial Board member Hamid Reza Karimi under the direction of Editor Hyungbo Shim.

This work is supported by National Natural Science Foundation of China (61174213, 61203074), the Program for New Century Excellent Talents in University (NCET-10-0665), the Fundamental Research Funds for the Central Universities (K5051370014).

Jian Wu received his B.Sc. degree from Fuyang Teachers College, Fuyang, China, and his M.Sc. degree from Xidian University, Xi’an, China, in 2009 and 2012, respectively. He is currently working toward a Ph.D. degree with the Department of Mathematics, Xidian University. His current research interests include nonlinear time-delay systems control and adaptive neural network backstepping control.

Weisheng Chen received his B.Sc. degree from Qufu Normal University, Qufu, China, and his M.Sc. and Ph.D. degrees from Xidian University, Xi’an, China, in 2000, 2004, and 2007, respectively. From 2008 to 2009, he was a Visiting Scholar with the Automation School, Southeast University, Nanjing, China. He is currently a Professor with the Department of Mathematics. He has authored or coauthored more than 50 journal and conference publications. His current research interests include neural networks, fuzzy systems, backstepping control, adaptive control, learning control for uncertain nonlinear systems such as time-delay or stochastic nonlinear systems, etc.

Jing Li is a Ph.D. and an Associate Professor in Xidian University, China. From Sep 2009 to Jul 2010, she was a Visiting Scholar with School of Control, Shandong University, China. From Oct 2011 to Oct 2012, she was an Academic Visitor with Plymouth University in Robotics and with the Imperial College London in human robot interaction respectively. Her current research interests include adaptive neural network control, stochastic control, robotics and humanrobot interaction.

Wenlong Ren received his M.Sc. degree from Xidian University, Xi’an, China, in 2013. His research interests include nonlinear systems control and adaptive backstepping control.

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Wu, J., Chen, W., Li, J. et al. Stabilization for a class of stochastic nonlinear systems with arbitrary switching via the common Lyapunov function method. Int. J. Control Autom. Syst. 11, 926–937 (2013). https://doi.org/10.1007/s12555-013-0037-5

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  • DOI: https://doi.org/10.1007/s12555-013-0037-5

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