Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120503-120503.doi: 10.1088/1674-1056/21/12/120503
张铁岩, 赵琰, 解相朋
Zhang Tie-Yan (张铁岩), Zhao Yan (赵琰), Xie Xiang-Peng (解相朋)
摘要: This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case, then the underlying nonlinear 2D system could be represented by the 2D Takagi-Sugeno (TS) fuzzy model which is convenient to implement the stability analysis. Secondly, a new kind of fuzzy Lyapunov function which is homogeneous polynomially parameter-dependent on fuzzy membership functions is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach to exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.
中图分类号: (Nonlinear dynamics and chaos)