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Abstract: The matrix converter (MC) presents a promising topology that will have to overcome certain barriers (protection systems, durability, the development of converters for real applications, etc.) in order to gain a foothold in the industry. In some applications, where continuous operation must be insured in the case of a system failure, improved reliability of the converter is of particular importance. In this sense, this article focuses on the study of a fault tolerant MC. The fault tolerance of a converter is characterized by its total or partial response in the case of a breakage of any of its components. Taking into consideration that virtually no work has been done on fault tolerant MCs, this paper describes the most important studies in this area. Moreover, a new method is proposed for detecting the breakage of MC semiconductors. Likewise, a new variation of SVM modulation with failure tolerance capacity is presented. This guarantees the continuous operation of the converter and the pseudo-optimum control of a PMSM. This paper also proposes a novel MC topology, which allows the flexible reconfiguration of this converter, when one or several of its semiconductors are damaged. In this way, the MC can continue operating at 100% of its performance without having to double its resources. In this way, it can be said that the solution described in this article represents a step forward towards the development of reliable matrix converters for real applications. [ABSTRACT FROM AUTHOR]