Stability Analysis using a Decrescent Quadratic Lyapunov Function

This paper presents the preliminary results of a method which proposes to assure the determination of the stability attributes of all linear and of a large class of nonlinear 1st and 2nd order systems. V(t,X,ß) = W(X)e^-ßt, a decrescent function is selected as the Lyapunov function, where W(X) is a general quadratic function of the state variables and ß ¿ 0. Initial results indicate that a good to an exact domain of attraction is achieved using the method presented in this paper. Four examples are included which demonstrate the application of the proposed hypothesis.