In the paper, we establish a new criterion for stability of system dx/dt =A(t)x, which is based on the assumption that one leading principal submatrixof order r and its complementary submatrix in A(t) both have eigenvalues withonly negative real parts. And also a feasible method for decomposition andaggregation of large-scale systems is provided.
本文应用系统的分解理论给出了保证非线性时变系统x_i=sum from (?) to (?)a_(ij)(t)x_j+f_i(t,x_1,x_2,x_3)(i=1,2,3)之零解为稳定的充分条件.由于本文不要求矩阵A(t)=(aij(t))_(3×3)的特征根均有负实部,因此,应用本文的结果讨论某些实际问题是方便的.
