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Abstract
This paper deals with the problem of H∞ control for 2-D non-linear system with stochastic perturbation. Based on spatial fuzzy set and inference mechanism, 2-D T-S fuzzy FMII model with stochastic perturbation is established first. Then the results for stability analysis and bounded real lemma are obtained. Moreover, an H∞ fuzzy controller is designed. In order to reduce the computational demand of the conditions for the existence of H∞ fuzzy controller, the control inputs are regarded as the variables independent of the states, and some free matrices are introduced to reduce the conservatism of this method. Then, a new H∞ fuzzy controller is derived. Two simulation examples are given to illustrate the effectiveness of the proposed approach.
Acknowledgements
The work described in this paper was supported by the National Natural Science Foundation of China (Grant No. 61074006).
Additional information
Notes on contributors
Xiaofeng Li
Xiaofeng Li received the MS degree in control science and engineering from Nanjing University of Science and Technology, China, in 2009. She is a Ph.D. student at Nanjing University of Science and Technology. Her research interests include 2-D systems, fuzzy systems and stochastic systems.
Weiqun Wang
Weiqun Wang received her Ph.D. degree from Nanjing University of Science and Technology, China, in 2003, majoring in automatic control. Her research interests are in the areas of 2-D systems, fuzzy systems and singular systems.
Lizhen Li
Lizhen Li received the B.Sc. degree in applied mathematics from Shanxi Datong University, Shanxi, in 2008. She is currently working toward the Ph.D. degree at Nanjing University of Science and Technology. Her current research interests include two-dimensional fuzzy control, robust control and optimal control.