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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 514504, 22 pages
http://dx.doi.org/10.1155/2012/514504
Research Article

Robust Adaptive Switching Control for Markovian Jump Nonlinear Systems via Backstepping Technique

1Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027, China
2Center of Information Science Experiment and Education, University of Science and Technology of China, China

Received 28 March 2012; Accepted 9 May 2012

Academic Editor: Xianxia Zhang

Copyright © 2012 Jin Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates robust adaptive switching controller design for Markovian jump nonlinear systems with unmodeled dynamics and Wiener noise. The concerned system is of strict-feedback form, and the statistics information of noise is unknown due to practical limitation. With the ordinary input-to-state stability (ISS) extended to jump case, stochastic Lyapunov stability criterion is proposed. By using backstepping technique and stochastic small-gain theorem, a switching controller is designed such that stochastic stability is ensured. Also system states will converge to an attractive region whose radius can be made as small as possible with appropriate control parameters chosen. A simulation example illustrates the validity of this method.