Linear flux observers for induction motors with quadratic Lyapunov certificates

We propose a full order Linear Time-Varying (LTV) Luenberger observer for the rotor flux estimation of an induction motor. Introducing a suitable reduced-order Linear-Time-Invariant (LTI) system that is always observable and controllable, we show that any arbitrary LTI design and its quadratic Lyapunov certificates can be lifted to the higher-order original LTV dynamics obtaining the same certificates. As a result, we show that arbitrary global uniform exponential bounds can be imposed on the estimation error, regardless of the rotor speed. Then applying a suitable order reduction technique, we build a reduced observer providing the same guarantees. We also establish interesting connections between these reduced observers and existing non-adaptive observers. We also show applications of our results when wanting to minimize the effects of measurement noise on the estimates.