Stability and boundedness of differential equations relative to initial time difference by employing vector Lyapunov functions

The existing stability results relative to initial time difference are not easy to be applied into practice since it is too hard to find a Lyapunov function satisfying all the conditions. This paper presents several quasi-stability criteria for nonlinear differential dynamical systems relative to initial time difference by employing vector Lyapunov functions. These new results might be more fruitful since it can satisfy less rigid requirements. As an application, the results are applied into a nonlinear dynamical system to get the quasi-stability properties.