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This study decribes the Tensor Product (TP) based model construction through the nonlinear dynamic system of the inverted pendulum. It presents the steps of TP modeling, various weighting functions and the Linear Matrix Inequality (LMI) based approach. LMI control has been used to stabilize the nonlinear system. This study shows the quasi-Linear Parameter-Varying (qLPV) state-space modeling and the Higher-Order Singular Value Decomposition (HOSVD) based TP model transformation. Some research in this issue already exists, but only the furuta, rotary, single and parallel-type double pendulum have been examined. In this paper the TP model transformation of the inverted pendulum is analyzed in terms of stability.

Study of the TP transformation via the inverted pendulum example