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

作　　者：张铁岩 赵琰 解相朋 

机构地区：[1]Department of Electrical Engineering,Shenyang Institute of Engineering

出　　处：《Chinese Physics B》2012年第12期109-117,共9页中国物理B（英文版）

基　　金：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);the Science and Technology Program of Shenyang (Grant No.F11-264-1-70)

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 ease 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 conser- vative 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.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 ease 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 conser- vative 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.

关 键 词：stability analysis Roesser model two-dimensional nonlinear systems parameter- dependent Lyapunov function 

分 类 号：TB112[理学—数学]