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This article proposes an alternative for robust control of synchronous reluctance motors using linear matrix inequalities to obtain fixed gains that ensure current and speed regulation, under parameter uncertainties and variations. The proposed design procedure is based on a polytopic model, which takes into account: i) uncertainties and variations of the mechanical and electrical parameters of the motor, ii) one step delay from digital implementation of the control law, and iii) internal model based controllers to guarantee reference tracking. Less conservative linear matrix inequalities, relying on slack variables, ensure robust pole location and certify the closed-loop stability for the entire domain of uncertain and time-varying motor parameters, based on parameter-dependent Lyapunov functions. The linear matrix inequalities ensure a fast and systematic computation of the control gains, that are also easy to be implemented, not adding computational complexity when compared, for instance, to usual strategies based on PI controllers. Experimental results for a 2.2 kW commercial motor are provided, validating the proposed procedure, and illustrating good tracking of currents and speed references, with suitable dynamic responses and reduced cross-coupling effects, when compared to sliding mode and PI controllers. [ABSTRACT FROM AUTHOR]