三维非线性临界解析动态方程的局部渐近稳定性  

Local asymptotic stability of 3D nonlinear analytic dynamic systems in critical cases

作　　者：倪郁东[1] 辛云冰[2] 沈吟东[3] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009 [2]集美大学理学院,福建厦门361021 [3]华中科技大学控制科学与工程系,湖北武汉430074

出　　处：《中国科学技术大学学报》2007年第11期1378-1382,共5页JUSTC

基　　金：福建省自然科学基金(A0440005);国家自然科学基金(70671045)资助.

摘　　要：考察了三维非线性临界动态方程Z.=f(Z),f(0)=0,Df(0)=A,σ(A)={±ω.i,0},ω>0的局部渐近稳定性.首先在非奇异线性坐标变换和时间尺度变换下,将其化成标准形式.之后,运用形式级数法的思想,在f(Z)是解析的假设下,研究了三维自由动态方程Z.=f(Z)的李雅普诺夫V函数的构造问题,给出了确定李雅普诺夫V函数的方法,并得到了判别三维解析动态方程局部渐近稳定的一组充分条件.The local asymptotic stability of the 3D nonlinear analytic dynamic equation was studied, which is formulated as Z^·=f（Z）,f（0）=0,Df（0）=A, in the critical case of σ（A）={±ω·i,0}, ω〉0. The study consists of three stages. The first is to convert the formulation of the equation into the standard form under the transformation of the nonsingular linear coordinates and time-measure. The second is to analyze the constitution of the Lyapunov＇s V-function and to develop further a method for determining the V-function by the aid of the idea of form-series. The last stage is to obtain a sufficiency condition of the local asymptotic stability for the 3D nonlinear analytic dynamic equation.

关 键 词：非线性动态方程 临界条件 李雅普诺夫V函数 局部渐近稳定 

分 类 号：O175.13[理学—数学]