The sufficient condition of system matrix to find a Lyapunov function

This paper aims to derive the condition of a system matrix that Lyapunov candidate function can be found according to traditional given methodology. The conditions for two-order system have been found successfully using basic theory. The availability of results are extended to some nonlinear and time varying system. The derived result is helpful to And a Lyapunov function before doing tedious and complicated finding work. Using similar procedure, the further results are expected to be found for three-order system although its complication and difficulty.