On the new results of global exponential attractive set

Abstract

Abstract In this paper, the global exponential attractive sets of a class of continuous-time dynamical systems defined by x = f ( x ) , x ∈ R n are studied. The elements of main diagonal of matrix A are both negative numbers and zero, where matrix A is the Jacobian matrix d f d x of a continuous-time dynamical system defined by x = f ( x ) , x ∈ R n evaluated at the origin x 0 = ( 0 , 0 , … , 0 ) 1 × n . However, note that the former equations that we are searching for a global bounded region have a common characteristic: the elements of main diagonal of matrix A are all negative. As far as we know, very few papers have addressed this problem.