Abstract
This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.
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This work was partially supported by HKU RGC Grant 7137/09E, the National Natural Scinece Foundation of China (60825303, 60834003), the 973 project (2009CB320600), the Foundation for the Author of National Excellent Doctoral Dissertation of China (2007B4), and the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University), Ministry of Education.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Chen, X., Lam, J., Gao, H. et al. Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions. Multidim Syst Sign Process 24, 395–415 (2013). https://doi.org/10.1007/s11045-011-0166-z
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DOI: https://doi.org/10.1007/s11045-011-0166-z