中国物理B ›› 2014, Vol. 23 ›› Issue (4): 40701-040701.doi: 10.1088/1674-1056/23/4/040701

• GENERAL • 上一篇    下一篇

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

代小林   

  1. School of Mechanical, Electronic, and Industrial Engineering, University of Electric Science and Technology of China, Chengdu 610054, China
  • 收稿日期:2013-07-30 修回日期:2013-09-04 出版日期:2014-04-15 发布日期:2014-04-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61203057 and 51305066).

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

Dai Xiao-Lin (代小林)   

  1. School of Mechanical, Electronic, and Industrial Engineering, University of Electric Science and Technology of China, Chengdu 610054, China
  • Received:2013-07-30 Revised:2013-09-04 Online:2014-04-15 Published:2014-04-15
  • Contact: Dai Xiao-Lin E-mail:www_dxl@126.com,xldai_uest@163.com
  • About author:07.05.Mh
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61203057 and 51305066).

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摘要： This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. 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 provided to demonstrate the effectiveness of the proposed result.

关键词: stability analysis, Roesser-type two-dimensional system, slack matrix variable, reducing conservatism

Abstract: This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. 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 provided to demonstrate the effectiveness of the proposed result.

Key words: stability analysis, Roesser-type two-dimensional system, slack matrix variable, reducing conservatism

中图分类号:  (Neural networks, fuzzy logic, artificial intelligence)

  • 07.05.Mh