A unified definition for damping torque coefficient of synchronous machines is proposed in this paper according to the principle of synthetic damping coefficients deduced from the Lyapunov Theorem.

By using Lyapunov stability theorem, both the stability of closed-loop system and the asymptotical convergence of tracking errors are ensured.

Specifically, Lyapunov techniques are fused with LaSalle's Invariance Theorem to prove that the constructed nonlinear controllers achieve asymptotic regulation of the crane system.