CAJ | 학술논문

研究了基于模糊Lyapunov函数分析连续仿射模糊系统稳定性的方法.首先,对模糊系统局部模型的后件部分进行扩展处理,以便于借鉴齐次模糊模型的稳定性分析方法.然后,分别得到基于改进公共Lyapunov函数与模糊Lyapunov函数的系统稳定条件,该条件可表示为一组线性矩阵不等式.通过算例对所得稳定条件进行对比,结果表明:基于模糊Lyapunov函数得到的稳定条件与基于改进公共Lyapunov函数的相比具有较小保守性；对后件部分进行扩展处理后,尽管稳定性证明方法较简便,但与不进行后件处理得到的稳定条件相比,可行解范围有所减小.最后,为了增大模糊Lyapunov函数的应用范围,提出了对模糊空间进行划分的方法,该方法可对隶属度函数为三角形或梯形的模糊系统进行稳定性分析,得到了基于分段模糊Lyapunov函数的系统稳定条件,并通过算例验证了所提方法的有效性.
연구료기우모호Lyapunov함수분석련속방사모호계통은정성적방법.수선,대모호계통국부모형적후건부분진행확전처리,이편우차감제차모호모형적은정성분석방법.연후,분별득도기우개진공공Lyapunov함수여모호Lyapunov함수적계통은정조건,해조건가표시위일조선성구진불등식.통과산례대소득은정조건진행대비,결과표명:기우모호Lyapunov함수득도적은정조건여기우개진공공Lyapunov함수적상비구유교소보수성；대후건부분진행확전처리후,진관은정성증명방법교간편,단여불진행후건처리득도적은정조건상비,가행해범위유소감소.최후,위료증대모호Lyapunov함수적응용범위,제출료대모호공간진행화분적방법,해방법가대대속도함수위삼각형혹제형적모호계통진행은정성분석,득도료기우분단모호Lyapunov함수적계통은정조건,병통과산례험증료소제방법적유효성.
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems.First,a method is introduced to deal with the consequent part of the fuzzy local model.Thus,the stability analysis method of the homogeneous fuzzy system can be used for reference.Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions,respectively.The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples.Compared with the method which does not expand the consequent part,the proposed method is simpler but its feasible region is reduced.Finally,in order to expand the application of the fuzzy Lyapunov functions,the piecewise fuzzy Lyapunov function is proposed,which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions.A numerical example validates the effectiveness of the proposed approach.