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# Stability Analysis and Control Design for 2-D Fuzzy Systems via Basis-dependent Lyapunov Functions

• ##### James Lam
Multidimensional Systems and Signal Processing (Impact Factor: 0.86). 10/2011; DOI: 10.1007/s11045-011-0166-z

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 (FMLSS) 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 inequal-ity (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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