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Mathematical Problems in Engineering
Volume 2016, Article ID 5185784, 11 pages
Research Article

Robust Stability, Stabilization, and Control of a Class of Nonlinear Discrete Time Stochastic Systems

1College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, Shandong 266510, China
2College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, China

Received 14 November 2015; Revised 20 March 2016; Accepted 31 March 2016

Academic Editor: Mingcong Deng

Copyright © 2016 Tianliang Zhang 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.


This paper studies robust stability, stabilization, and control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.