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The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect controldoi:10.3390/sym11101322 fatcat:i23b6ushjzhdzm4yg4izgqocsu