Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique

doi:10.1088/1674-1056/21/12/120503

Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120503-120503.doi: 10.1088/1674-1056/21/12/120503

Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique

张铁岩, 赵琰, 解相朋

Department of Electrical Engineering, Shenyang Institute of Engineering, Shenyang 110136, China

收稿日期:2012-04-01 修回日期:2012-05-30 出版日期:2012-11-01 发布日期:2012-11-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60972164, 60904101 and 61273029), the Key Project of Chinese Ministry of Education (Grant No. 212033), the Key Technologies R & D Program of Liaoning Province (Grant No. 2011224006), the Program for Liaoning Innovative Research Team in University (Grant No. LT2011019), the Program for Liaoning Excellent Talents in University (Grant No. LJQ2011137), and the Science and Technology Program of Shenyang (Grant No. F11-264-1-70).

Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique

Zhang Tie-Yan (张铁岩), Zhao Yan (赵琰), Xie Xiang-Peng (解相朋)

Department of Electrical Engineering, Shenyang Institute of Engineering, Shenyang 110136, China

Received:2012-04-01 Revised:2012-05-30 Online:2012-11-01 Published:2012-11-01
Contact: Zhang Tie-Yan E-mail:zty@sie.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 60972164, 60904101 and 61273029), the Key Project of Chinese Ministry of Education (Grant No. 212033), the Key Technologies R & D Program of Liaoning Province (Grant No. 2011224006), the Program for Liaoning Innovative Research Team in University (Grant No. LT2011019), the Program for Liaoning Excellent Talents in University (Grant No. LJQ2011137), and the Science and Technology Program of Shenyang (Grant No. F11-264-1-70).

摘要/Abstract

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.

关键词: stability analysis, Roesser model, two-dimensional nonlinear systems, parameter-dependent Lyapunov function

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, 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.

Key words: stability analysis, Roesser model, two-dimensional nonlinear systems, parameter-dependent Lyapunov function

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

张铁岩, 赵琰, 解相朋. Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique[J]. Chin. Phys. B, 2012, 21(12): 120503-120503.

Zhang Tie-Yan (张铁岩), Zhao Yan (赵琰), Xie Xiang-Peng (解相朋). Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique[J]. Chin. Phys. B, 2012, 21(12): 120503-120503.

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Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique

Stability analysis of nonlinear Roesser-type two-dimensional systems via homogenous polynomial technique

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