Generalized Lyapunov function for Liénard-type non-linear systems

A systematic procedure for the derivation of Lyapunov functions for non-linear systems given by Lienard's equation is proposed. To establish the procedure, a similar system is derived first, by multiplying both sides of the system by a transformation matrix. Then, stability criteria for the system, which introduce a generalized Lyapunov function, are presented. The Lyapunov function obtained is used to estimate the stability region of the system. The superiority of the proposed method is illustrated by applying it to a single-machine system, which includes the variable damping effect, comparing the results with those obtained by conventional methods.