[1] Pan JuntaoFei ShuminMu Chaoxu, Xue Mingxiang,. Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 550-553. [doi:10.3969/j.issn.1003-7985.2010.04.010]
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Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions(
)
基于新松弛条件的连续时间Takagi-Sugeno模糊系统镇定设计
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 26
- Issue:
- 2010 4
- Page:
- 550-553
- Research Field:
- Automation
- Publishing date:
- 2010-12-30
Info
- Title:
- Stabilization design for continuous-time Takagi-Sugeno fuzzy systemsbased on new relaxed conditions
- 基于新松弛条件的连续时间Takagi-Sugeno模糊系统镇定设计
- Author(s):
- Pan JuntaoFei ShuminMu Chaoxu; Xue Mingxiang
- Key Laboratory of Measurement and Control of Complex Systems of Engineering ofMinistry of Education, Southeast University, Nanjing 210096, China
- Keywords:
- Takagi-Sugeno fuzzy model; fuzzy Lyapunov function; staircase membership function; linear matrix inequality
- PACS:
- TP183
- DOI:
- 10.3969/j.issn.1003-7985.2010.04.010
- Abstract:
- This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno(T-S)fuzzy systems. New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model, the information of the membership functions can be brought into the stabilization design of the fuzzy systems, thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems. Unlike some previous fuzzy Lyapunov function approaches reported in the literature, the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. A simulation example is given to demonstrate the validity of the proposed approach.
- 研究了一类连续时间Takagi-Sugeno模糊系统的镇定控制器设计问题, 提出了一种新的基于模糊Lyapunov函数和阶梯隶属度函数的系统镇定条件.通过阶梯隶属度函数逼近原系统的隶属度函数, 系统隶属度函数信息被引入到其镇定设计中, 从而大大降低了现有T-S模糊控制系统镇定设计的保守性.与已有基于模糊Lyapunov函数的连续T-S模糊系统的镇定设计不同, 所提出的镇定条件不依赖于隶属度函数的导数, 因此具有较少保守性.此外, 所得镇定条件可表示为一组线性矩阵不等式, 而不是双线性矩阵不等式, 因而可以利用凸优化算法方便地进行求解.仿真实例表明了所提方法的有效性.
References:
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[7] Guerra T M, Vermeiren L. LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi-Sugeno’s form [J]. Automatic, 2004, 40(5): 823-829.
[8] Rhee B J, Won S. A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design [J]. Fuzzy Sets and Systems, 2006, 157(9): 1211-1228.
[9] Sala A, Arino C. Relaxed stability and performance LMI conditions for Takagi-Sugeno systems with polynomial constraints on membership function shapes [J]. IEEE Transactions on Fuzzy Systems, 2008, 16(5): 1328-1336.
[10] Lam H K, Narimani M. Quadratic-stability analysis of fuzzy-model-based control systems using staircase membership functions [J]. IEEE Transactions on Fuzzy Systems, 2010, 18(1): 125-137.
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Memo
- Memo:
-
Biographies: Pan Juntao(1983—), male, graduate; Fei Shumin(corresponding author), male, doctor, professor, smfei@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.60764001, 60835001, 60875035, 61004032), the Postdoctoral Research Fund of Southeast University, the Natural Science Foundation of Jiangsu Province(No.BK2008294).
Citation: Pan Juntao, Fei Shumin, Mu Chaoxu, et al. Stabilization design for continuous-time Takagi-Sugeno fuzzy systems based on new relaxed conditions[J].Journal of Southeast University(English Edition), 2010, 26(4):550-553.