A minimum-time torque control strategy for permanent-magnet AC motor drives is presented. The proposed technique neither requires the solution of a HJB-type equation, which would be practically unfeasible, nor uses Pontryagin's maximum principle. Instead, the solution is obtained by an ad hoc procedure based oil the computation of reachability and controllability sets. In principle, the optimal control strategy can be carried out by iteratively solving a fourth-degree polynomial equation. For its efficient implementation, an algorithm based on Sturm sequences is suggested. The sequence of online operations required by the algorithm for a given tolerance on the optimal time is illustrated. The method has been tested on a laboratory prototype. Experimental results show the effectiveness of the technique. (C) 2007 Elsevier Ltd. All rights reserved.