Modified variable gradient method for constructing the Lyapunov function using nonlinear programming method

In this paper, is used nonlinear programming method to modify the well-known variable gradient method for constructing the Lyapunov function of a system of ordinary differential equations. Thereafter the problem is formulated as a nonlinear optimization problem to evaluate the real symmetric matrix used in the definition of the quadratic form Lyapunov function by way of examples, we demonstrate the applicability of the method problem.