离散模糊双线性系统的稳定控制

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (10): 2440-2444.

离散模糊双线性系统的稳定控制

张果, 李俊民

西安电子科技大学理学院, 陕西, 西安, 710071

收稿日期:2008-09-03 修回日期:2008-10-23 出版日期:2009-10-20 发布日期:2010-01-03
作者简介:张果(1972- ),女,博士研究生,主要研究方向为鲁棒、模糊控制.E-mail:zhangguo163163@163.com
基金资助:
国家自然科学基金(60374015)资助课题

Stabilizing control for discrete-time fuzzy bilinear systems

ZHANG Guo, LI Jun-min

School of Science, Xidian Univ., Xi'an 710071, China

Received:2008-09-03 Revised:2008-10-23 Online:2009-10-20 Published:2010-01-03

摘要/Abstract

摘要： 提出了一种对一类离散模糊双线性系统(discrete-time fuzzy bilinear system,DFBS)稳定控制的新方法.首先,把DFBS转换成一个等价的切换DFBS.然后,基于分段Lyapunov函数,同时考虑同一个子空间内不同模糊子系统之间的相互作用,得到了闭环系统放松的渐近稳定的充分条件.采用锥补线性化(cone complemen-tarity linearization,CCL)算法将控制器的设计转化成一个受线性矩阵不等式(linear matrix inequality,LMI)约束的最小化问题.最后,由仿真数例说明了所提方法的有效性.

Abstract: A new approach of stability analysis and synthesis for discrete-time fuzzy bilinear system(DFBS) is presented.First,the DFBS is transformed to an equivalent switching DFBS.Consequently,based on the piecewise Lyapunov function and considered the interactions among the fuzzy subsystems in each subregion,the relaxed stabilization conditions are derived for the switching DFBS.The cone complementarity linearization(CCL) algorithm is employed to convert the controller design into a minimum problem with linear matrix inequality(LMI) constraints.Finally,a simulation example shows that the approach is effective.

中图分类号:

TP13

张果, 李俊民. 离散模糊双线性系统的稳定控制[J]. Journal of Systems Engineering and Electronics, 2009, 31(10): 2440-2444.

ZHANG Guo, LI Jun-min. Stabilizing control for discrete-time fuzzy bilinear systems[J]. Journal of Systems Engineering and Electronics, 2009, 31(10): 2440-2444.

参考文献

[1] Wang R J,Lin W W,Wang W J.Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems[J].IEEE Trans.on System,Manand Cybernetics,2004,34(2):1288-1292.
[2] Tseng C S,Chen B S,Uang H J.Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model[J].IEEE Trans.on Fuzzy Syst.,2001,9(3):381-392.
[3] Chen B,Liu X P.Fuzzy guaranteed cost control for nonlinear systems with time-varying delay[J].IEEE Trans.on Fuzzy Systems,2005,13(2):238-249.
[4] 张果,李俊民,吴明山.不确定时滞模糊系统的鲁棒H_∞静态输出反馈控制[C]//Proc.of the 27th Chinese Control Conference,Kunming,China,2008:626-631.
[5] Feng G.Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions[J].IEEE Trans.on Fuzzy Systems,2004,12(1):22-28.
[6] Chen C L,Feng G.Delay-dependent piecewise control for timedelay T-S fuzzy systems with application to chaos control[C]//The IEEE International Conference on Fuzzy Systems,2005:1056-1061.
[7] Wang W J,Chan Y J,Sun C H.Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function[J].IEEE Trans.on Systems,Man and Cybernetics,2007,37(3):551-559.
[8] Li T H S,Tsai S H.T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems[J].IEEE Trans.on Fuzzy Systems,2007,3(15):494-505.
[9] Tsai S H,Li T H S.Robust fuzzy control of a class of fuzzy bilinear systems with time-delay[J].Chaos,Solitons and Fractals,2009,39(5):2028-2040.
[10] Li T H S,Tsai S H,Lee J Z,et al.Robust H_∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems[J].IEEE Trans.on System,Man and Cybernetics,2008,38(2):510-526.
[11] Goh K C,Turan L,GSafonov M,et al.Baffine matrix inequality properties and computational methods[C]//Proc.of American Control Conference,1994:850-855.

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