The induction motor is widely utilized in industry and exists in a plethora of applications. Until the last 20 years or so, it was primarily used in an open-loop fashion (i.e., balanced sinusoidal voltages, constant load torque and viscous friction) with its inherent stability counted on to allow operation over a wide range of operating conditions. Unlike classical arguments based on the steady-state torque-slip curve, a rigorous analytical stability argument using the full nonlinear dynamical model is presented. In particular, conditions for global asymptotic stability of the induction motor in the sense of Lyapunov are given in terms of the motor parameters, operating slip, and synchronous frequency.
Oteafy, Ahmed and Chiasson, John. (2010). "A Study of the Lyapunov Stability of an Open-Loop Induction Machine". IEEE Transactions on Control Systems Technology, 18(6), 1469-1476. http://dx.doi.org/10.1109/tcst.2009.2039796