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In this paper, a new method is presented for the study of the stability of a second-order thyristor device control system; the current loop of a separately excited dc motor is considered in particular. Nonlinear discrete mathematical models are proposed for continuous and discontinuous operations. For local analysis, exact analytical formulas are given by linearization of the equations around the considered operating point. Graphical methods are proposed for the global behavior of the system which allow us to study the nonlinear effects, for example, the subharmonics appearing when the system becomes unstable. For accurate results, these graphical methods are transposed to simple digital computer programs.