Lyapunov functions are a mathematical generalization of the dissipative energy concept of
physics. Lyapunov functions are the centerpiece of the Lyapunov-stability theory for
dynamical systems in general. Here we present a simple method for checking the validity of
a quadratic Lyapunov function, which is constructed for the linearization of a nonlinear
system and does not in general satisfy the condition of having a negative orbital derivative
on the origins basin of attraction. The current work also extends previous work done on …