Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique |
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| Authors: | Zhang Tie-Yan Zhao Yan and Xie Xiang-Peng |
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| Affiliation: | Department of Electrical Engineering, Shenyang Institute of Engineering, Shenyang 110136, China |
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| Abstract: | 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 so that the underlying nonlinear 2D system can be represented by the 2D Takagi-Sugeno(TS) fuzzy model,which is convenient for implementing the stability analysis.Secondly,a new kind of fuzzy Lyapunov function,which is a 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 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. |
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| Keywords: | stability analysis Roesser model two-dimensional nonlinear systems parameter- dependent Lyapunov function |
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