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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 235804, 11 pages
Research Article

Robust Fuzzy Control for Nonlinear Discrete-Time Stochastic Systems with Markovian Jump and Parametric Uncertainties

College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

Received 4 May 2014; Revised 2 August 2014; Accepted 3 August 2014; Published 18 August 2014

Academic Editor: Peng Shi

Copyright © 2014 Huiying Sun and Long Yan. 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.


The paper mainly investigates the fuzzy control problem for a class of nonlinear discrete-time stochastic systems with Markovian jump and parametric uncertainties. The class of systems is modeled by a state space Takagi-Sugeno (T-S) fuzzy model that has linear nominal parts and norm-bounded parameter uncertainties in the state and output equations. An control design method is developed by using the Lyapunov function. The decoupling technique makes the Lyapunov matrices and the system matrices separated, which makes the control design feasible. Then, some strict linear matrix inequalities are derived on robust norm conditions in which both robust stability and performance are required to be achieved. Finally, a computer-simulated truck-trailer example is given to verify the feasibility and effectiveness of the proposed design method.