وحید میگلی

This paper introduces a novel approach to the stability analysis of nonlinear systems using the Lyapunov function candidates. This approach focuses on the negative definiteness of the derivative of the Lyapunov function candidate, instead of positive-definiteness of the function itself. Determining such a Lyapunov function candidate, and with a sign test on Lyapunov function, the stability of zero equilibrium state (ZES) of the systems is assessed. In this new approach, a Lyapunov function candidate is constructed as a linear combination of some basic functions. The coefficients of this linear combination have to be determined such that the derivative of the resulting Lyapunov candidate becomes negative definite. Also, an algebraic approach to form such linear combination for zero order homogeneous polynomial systems is provided which generalizes the Lyapunov equation in the stability analysis of the linear systems.