On the new results of global exponential attractive set

Abstract

In this paper, the global exponential attractive sets of a class of continuous-time dynamical systems defined by $\dot{x}=f\left(x\right),x\in R^n$ are studied. The elements of main diagonal of matrix $A$ are both negative numbers and zero, where matrix $A$ is the Jacobian matrix $\frac{df}{dx}$ of a continuous-time dynamical system defined by $\dot{x}=f\left(x\right),x\in R^n$ evaluated at the origin $x_0={(0,0,\dots ,0)}_{1\times n}$. 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.