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A sensorless speed tracking control scheme for permanent-magnet synchronous motors (PMSMs) is presented in this paper. This efficient scheme provides the exponential convergence on estimation errors of rotor's speed and position, and tracking error of rotor's speed. First, the Takagi-Sugeno fuzzy model is used to represent the nonlinear system of PMSMs. Then, a state observer is constructed to estimate the rotor's speed and position in the manner of exponentially convergent rate. For converting the tracking control into a stabilization problem, a new and novel control design called virtual-desired variable synthesis is proposed to define the internal desired states. Consequently, the practical controller is derived under some adequate assumptions; meanwhile, the feedback gains and the observer gains are obtained separately by solving a set of linear matrix inequalities pertaining to system stability. The performance of the proposed sensorless algorithm is verified by experiments of PMSMs for speed tracking.