The paper demonstrates a tensor product (TP) model transformation-based framework for an induction machine (IM). The state space model of an IM is highly nonlinear, thus the Takagi–Sugeno (TS) fuzzy model-based quasi-linear parameter-varying (qLPV) representation can be a good alternative approach of machines modeling. The paper presents the basics of IM state space modeling, how the TP transformation can be applied in details. The control of IM is always a pivotal point; hence, options of feedback control are discussed. The main goal of this paper is to present the whole process of IM TP transformation-based modeling including a control system.