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Novel stabilization conditions for discrete-time 2-D T-S fuzzy systems in the second FM model

This paper is concerned with the problem of stabilization of the discrete-time nonlinear 2-D system described by the second Fornasini and Marchesini (FM) state-space model which plays an important role in many practical applications. Firstly, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Secondly, a edgewise subdivision algorithm is applied to implement the simplex edgewise subdivision which divides the overall 2-D fuzzy systems into a lot of sub-systems by a kind of algebraic description. These sub-systems have the same volume and shape characteristics. Thirdly, based on the attained algorithm, a novel kind of switching controller which switches by the transfer of different operating sub-systems is proposed to stabilize the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.